GRK 1269:  Global Structures in Geometry and Analysis

• Subject Area: Mathematics
• Term: from 2006 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 968940

• Final Report Year: 2015

Final Report Abstract

No abstract available

Publications

• A Decomposition of the Moving Cone of a Projective Manifold According to the Harder-Narasimhan Filtration of the Tangent Bundle
  Sebastian Neumann
  
• A Variational Problem Leading to a Singular Elliptic Equation Involving the 1-Laplacian
  Florian Krügel
  
• An Evolution Equation Involving the Normalized p-Laplacian
  Kerstin Does
  
• Arithmetic and Asymptotic Properties of Mock Theta Functions and Mock Jacobi Forms
  Matthias Waldherr
  
• Asymptotic Behaviour of Higher Eigenfunctions of the p-Laplacian as p goes to 1
  Enea Parini
  
• Automorphe Produkte singulären Gewichts
  Heike Hagemeier
  
• Automorphic Products on Unitary Groups
  Eric Hofmann
  
• Compression of Nakajima Monomials of Type A and C
  Matthias Meng
  
• Constructions of Open Books and Applications of Convex Surfaces in Contact Topology
  Mirko Klukas
  
• Eigenvalue Problem for the 1-Laplace Operator
  Zoja Milbers
  
• Evolution of Geometries with Torsion
  Sebastian Stock
  
• Explicit Symplectic Packings: Symplectic Tunneling and new Maximal Constructions
  Ingo Wieck
  
• Families of Canonically Polarized Manifolds over log Fano varieties
  Daniel Lohmann
  
• Generalized Gradients of G-Structures and Kählerian Twistor Spinors
  Mihaela Pilca
  
• Generalized Sections and Representations of Copolarity One and Two
  Carolin Pomrehn
  
• Harmonic Maass Forms, Jacobi Forms, and Applications to Lie Superalgebras
  René Olivetto
  
• Homological Description of Crystal Structures on Quiver Varieties
  Schumann, Beatrix
  
• Hopf’s Type Estimates near Singular Boundary Points
  Maryam Beygmohammadi
  
• L2 -Cohomology of Coverings
  Stephan Gareis
  
• Lipschitz Solutions for a 1-Dimensional Fast Diffusion Equation
  Nicole Schadewaldt
  
• Mock Modular Forms and Class Numbers of Quadratic Forms
  Michael Mertens
  
• Morse Inequalities and Bergman Kernels
  Wen Lu
  
• On the Lifetime of a Conditioned Brownian motion
  Matthias Erven
  
• One-skeleton Galleries and Cell Combinatorics
  An Noa Nguyen
  
• Positivity Preserving Properties of Biharmonic Boundary Value Problems on Domains with Corners
  Athanasios Stylianou
  
• Projective Resolutions, Periodicity and Local Algebras
  Stefanie Pauly (Küpper)
  
• Sasakian Manifolds: Differential Forms, Curvature and Conformal Killing Forms
  Christian Stromenger
  
• Surfaces of Minimal Complexity in Low-Dimensional Topology
  Matthias Nagel
  
• Taut Manifolds and Foliations
  Stephan Wiesendorf
  
• The Analytic Torsion on Manifolds with Boundary and Conical Singularities
  Boris Vertman
  
• The Cone of Moving Curves on Algebraic Varieties
  Sammy Barkowski
  
• The Symplectic Plactic Monoid, Words, MV Cycles, and non-Levi Branchings
  Jacinta Pérez Gavilán Torres
  
• An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold admitting parallel one-form, J. Geom. Phys., 28 (1998), 263–270
  B. Alexandrov, G. Grantcharov, S. Ivanov
  
• Curvature Properties of Twistor Spaces of Quaternionic Kähler Manifolds, J. Geom., 62 (1998), 1–12
  B. Alexandrov, G. Grantcharov, S. Ivanov
  
• Dirac operators on Hermitian spin surfaces, Ann. Glob. Anal. Geom., 18 (2000), 529–539
  B. Alexandrov, S. Ivanov
  
• The Dolbeault operator on Hermitian spin surfaces, Ann. Inst. Fourier, 51 (2001), 221–235
  B. Alexandrov, S. Ivanov
  
• The Dolbeault operator on Hermitian spin surfaces, Ann. Inst. Fourier, 51 (2001), 221–235
  B. Alexandrov, G. Grantcharov, S. Ivanov
  
• Vanishing theorems on Hermitian manifolds, Diff. Geom. Appl. 14 (2001), 251–265
  B. Alexandrov, S. Ivanov
  
• Hyper-Hermitian quaternionic Kähler manifolds, Ann. Glob. Anal. Geom., 22 (2002), 75–98
  B. Alexandrov
  
• Weyl structures with positive Ricci tensor, Diff. Geom. Appl., 18 (2003), 343–350
  B. Alexandrov, S. Ivanov
  
• Hermitian spin surfaces with small eigenvalues of the Dolbeault operator, Ann. Inst. Fourier, 54 (2004), 2437–2453
  B. Alexandrov
  
• Almost Hermitian 6-manifolds revisited, J. Geom. Phys., 53 (2005), 1–30
  B. Alexandrov, T. Friedrich, N. Schoemann
  
• On contact p-spheres, Ann. Inst. Fourier 55 (2005), 1167–1194
  M. Zessin
  
• On weak holonomy, Math. Scand., 96 (2005), 169–189
  B. Alexandrov
  
• Sp(n)U (1)-connections with parallel totally skew-symmetric torsion, J. Geom. Phys. 57 (2006), 323–337
  B. Alexandrov
  
• Explicit solutions of the equation −div z = f under the side-constraint ||z|| ∞ = 1. Proc. Appl. Math. Mech., 7: 1060901–1060902 (2007)
  Z. Milbers
  
• On contact tops and integrable tops. Indag. Math., New Ser., 18 (2007), 305–325
  M. Zessin
  
• Satisfiability of algebraic circuits over sets of natural numbers. FSTTCS 2007: Foundations of software technology and theoretical computer science, 253–264, Lecture Notes in Comput. Sci., 4855, Springer, Berlin, 2007
  Ch. Glaßer, Ch. Reitwießner, St. Travers, M. Waldherr
  
• The first eigenvalue of the Dirac operator on locally reducible Riemannian manifolds, J. Geom. Phys. 57 (2007), 467–472
  B. Alexandrov
  
• Appendix to "K. Kirsten, P. Loya, J. Park, Exotic expansions and pathological properties of zeta-functions on conic manifolds". J. Geom. Anal. 18 (2008), 835-888
  B. Vertman
  
• Numerical variational methods applied to cylinder buckling, SIAM J. Sci. Comput., 30 (2008), 1362–1386
  J. Horák , G. J. Lord, M. A. Peletier
  
• On the asymptotics of solutions of the Lane-Emden problem for the p-Laplacian. Arch. Math. (Basel) 91 (2008), no. 4, 354–365
  Ch. Grumiau, E. Parini
  
• On the lifetime of a conditioned Brownian motion on a fish bowl. Arch. Math. (Basel) 90 (2008), no. 1, 87–96
  M. Erven, G. Sweers
  
• A minimax theorem in the presence of unbounded Palais-Smale sequences, Isr. J. Math., 172 (2009), 125–143
  J. Horák, M. Lucia
  
• Analytic torsion of a bounded generalized cone. Comm. Math. Phys. 290 (2009), no. 3, 813–860
  B. Vertman
  
• Lifting SU (3)-structures to nearly parallel G2 -structures. J. Geom. Phys. 59 (2009), no. 1, 1–7
  S. Stock
  
• Lifting SU (3)-structures to nearly parallel G2-structures. J. Geom. Phys., 59(1) (2009)
  S. Stock
  
• On the positivity preserving property of hinged plates. SIAM J. Math. Anal. 41 (2009), no. 5, 2031–2037
  E. Parini, A. Stylianou
  
• Rationally connected foliations on surfaces. Doc. Math. 14 (2009), 157–165
  S. Neumann
  
• Refined analytic torsion on manifolds with boundary. Geom. Topol. 13 (2009), no. 4, 1989–2027
  B. Vertman
  
• Very weak solutions with boundary singularities for semilinear elliptic Dirichlet problems in domains with conical corners, J. Math. Anal. Appl., 352 (2009), 496–514
  J. Horák, P. J. McKenna, W. Reichel
  
• Zeta determinants for regular-singular Laplace-type operators. J. Math. Phys. 50 (2009), no. 8, 083515
  B. Vertman
  
• Comparing hinged and supported rectangular plates, Comptes Rendus Mecanique 338 (2010) pp. 489-492
  A. Styliano, G. Sweers
  
• Counting Zariski chambers on del Pezzo surfaces. J. Algebra 324 (2010), no. 1, 92–101
  T. Bauer, M. Funke, S. Neumann
  
• Deformations along subsheaves. Enseign. Math. (2) 56 (2010), no. 3-4, 287–313
  St. Kebekus, St. Kousidis, D. Lohmann
  
• Existence of a sequence of eigensolutions for the 1-Laplace operator. J. Lond. Math. Soc. (2) 82 (2010), no. 1, 74–88
  Z. Milbers, F. Schuricht
  
• Limits as p → ∞ of p-Laplacian problems with a superdiffusive power-type nonlinearity: positive and sign-changing solutions. J. Math. Anal. Appl. 372 (2010), no. 2, 629–644
  F. Charro, E. Parini
  
• Matthias Equivalence problems for circuits over sets of natural numbers. Theory Comput. Syst. 46 (2010), no. 1, 80–103
  Ch. Glaßer, K. Herr, Ch. Reitwießner, St. Travers, M. Waldherr
  
• On a fixed point in the metric space of normalized Hausdorff moment sequences. Rend. Circ. Mat. Palermo (2) Suppl. No. 82 (2010), 251–257
  Ch. Berg, M. Beygmohammadi
  
• Satisfiability of algebraic circuits over sets of natural numbers. Discrete Appl. Math. 158 (2010), no. 13, 1394–1403
  Ch. Glaßer, Ch. Reitwießner, St. Travers, M. Waldherr
  
• The cone of moving curves of a smooth Fano three- or fourfold. Manuscripta Math. 131 (2010), no. 3-4, 305–322
  S. Barkowski
  
• The second eigenvalue of the p-Laplacian as p goes to 1. Int. J. Differ. Equ. 2010, Article ID 984671, 23 pages
  E. Parini
  
• Two fixed-point theorems for mappings satisfying a general contractive condition of integral type in the modular space. Int. J. Math. Math. Sci. 2010, Art. ID 317107, 10 pp.
  M. Beygmohammadi, A. Razani
  
• A Maass lifting of Θ3 and class numbers of real and imaginary quadratic fields. Math. Res. Lett. 18 (2011), no. 5, 1001–1012
  R.C. Rhoades, M. Waldherr
  
• A new proof of Branson’s classification of elliptic generalized gradients. Manuscripta Math. 136 (2011), no. 1-2, 65–81
  M. Pilca
  
• A note on the conformal invariance of G-generalized gradients. Internat. J. Math. 22 (2011), no. 11, 1561–1583
  M. Pilca
  
• A representation-theoretical proof of Branson’s classification of elliptic generalized gradients. Differential Geom. Appl. 29 (2011), suppl. 1, S188–S195
  M. Pilca
  
• An evolution equation involving the normalized p-Laplacian. Commun. Pure Appl. Anal. 10 (2011), no. 1, 361–396
  K. Does
  
• An introduction to the Cheeger problem. Surv. Math. Appl. 6 (2011), 9–21
  E. Parini
  
• Continuity of the variational eigenvalues of the p-Laplacian with respect to p. Bull. Aust. Math. Soc. 83 (2011), no. 3, 376–381
  E. Parini
  
• Fixed point theorems in modular spaces. Math. Commun. 16 (2011), no. 1, 13–20
  A.P. Farajzadeh, M. Beyg Mohammadi, M.A. Noor
  
• Global attractor for some wave equations of pand p (x)-Laplacian type. Differential Integral Equations 24 (2011), no. 1-2, 159–176
  N.M. Stavrakakis, A.N. Stylianou
  
• Kählerian twistor spinors. Math. Z. 268 (2011), no. 1-2, 223–255
  M. Pilca
  
• Numerical investigation of the smallest eigenvalues of the p-Laplace operator on planar domains. Electron. J. Differential Equations 2011, No. 132
  J. Horák
  
• On certain explicit congruences for mock theta functions. Proc. Amer. Math. Soc. 139 (2011), no. 3, 865–879
  M. Waldherr
  
• On paradoxes in problems of the bending of polygonal plates with “hinge-supported” edges. Dokl. Akad. Nauk 439 (2011), no. 4, 476–480
  S.A. Nazarov, G. Kh. Svirs, A. Stilyanou
  
• Regular singular Sturm-Liouville operators and their zetadeterminants. J. Funct. Anal. 261 (2011), no. 2, 408–450
  M. Lesch, B. Vertman
  
• Remarks on the product of harmonic forms. Pacific J. Math. 250 (2011), no. 2, 353–363
  L. Ornea, M. Pilca
  
• Some special aspects related to the 1-Laplace operator. Adv. Calc. Var. 4 (2011), no. 1, 101–126
  Z. Milbers, F. Schuricht
  
• The microstructure of Lipschitz solutions for a one-dimensional logarithmic diffusion equation. Comment. Math. Univ. Carolin. 52 (2011), no. 2, 227–255
  N. Schadewaldt
  
• Analytic torsion on manifolds with edges. Adv. Math. 231 (2012), no. 2, 1000–1040
  R. Mazzeo, B. Vertman
  
• Compression of Nakajima monomials in type A and C. J. Algebraic Combin. 35 (2012), no. 4, 649–690
  M. Meng
  
• Corners give problems when decoupling fourth order equations into second order systems. SIAM J. Numer. Anal. 50 (2012), no. 3, 1604–1623
  T. Gerasimov, A. Stylianou, G. Sweers
  
• Deformations of nearly parallel G2 -structures. Asian J. Math. 16 (2012), 713–744
  B. Alexandrov, U. Semmelmann
  
• Hinged and supported plates with corners. Z. Angew. Math. Phys. 63 (2012), no. 5, 929–960
  S.A. Nazarov, A. Stylianou, G. Sweers
  
• On formal Riemannian metrics. An. Ştiinţ. Univ. Övidius Constanţa Ser. Mat. 20 (2012), no. 2, 131–144
  M. Pilca
  
• The metric anomaly of analytic torsion at the boundary of an even dimensional cone. Ann. Global Anal. Geom. 41 (2012), no. 1, 61–90
  B. Vertman
  
• Asymptotics for moments of higher ranks. Int. J. Number Theory 9 (2013), no. 3, 675–712
  M. Waldherr
  
• Borcherds products for U(1,1). Int. J. Number Theory 9 (2013), no. 7, 1801–1820
  E. Hofmann
  
• Families of canonically polarized manifolds over log Fano varieties. Compos. Math. 149 (2013), no. 6, 1019–1040
  D. Lohmann
  
• Higher rank homogeneous Clifford structures. J. Lond. Math. Soc. (2) 87 (2013), no. 2, 384–400
  A. Moroianu, Andrei, M. Pilca
  
• Homogeneous almost quaternion- Hermitian manifolds. Math. Ann. 357 (2013), no. 4, 1205–1216
  A. Moroianu, M. Pilca, U. Semmelmann
  
• Knuth relations, tableaux and MV- cycles. J. Ramanujan Math. Soc. 28A (2013), 191–219
  St. Gaussent, P. Littelmann, An Hoa Nguyen
  
• Limits as p → ∞ of p-Laplacian eigenvalue problems perturbed with a concave or convex term. Calc. Var. Partial Differential Equations 46 (2013), no. 1-2, 403–425
  F. Charro, E. Parini
  
• Necessary condition for eigensolutions of the 1-Laplace operator by means of inner variations. Math. Ann. 356 (2013), no. 1, 147–177
  Z. Milbers, F. Schuricht
  
• On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves. Integers 13 (2013), Paper No. A15, 16 pp.
  M. Kirschmer, M.H. Mertens
  
• On prolongations of contact manifolds. Proc. Amer. Math. Soc. 141 (2013), no. 9, 3257–3263
  M. Klukas, B. Sahamie
  
• The exotic heat-trace asymptotics of a regular-singular operator revisited. J. Math. Phys. 54 (2013), no. 6, 063501
  B. Vertman
  
• A new proof of a Bismut-Zhang formula for some class of representations. Geometric and spectral analysis, 1–14, Contemp. Math., 630, Amer. Math. Soc., Providence, RI, 2014
  M. Braverman, B. Vertman
  
• Automorphism groups of hyperbolic lattices. J. Algebra 408 (2014), 147–165
  M.H. Mertens
  
• Borcherds products on unitary groups. Math. Ann. 358 (2014), no. 3-4, 799–832
  E. Hofmann
  
• Elliptic theory of differential edge operators, II: Boundary value problems. Indiana Univ. Math. J. 63 (2014), no. 6, 1911–1955
  R. Mazzeo, B. Vertman
  
• Hopf’s boundary point lemma, the Krein-Rutman theorem and a special domain. Positivity 18 (2014), no. 1, 81–94
  M. Beygmohammadi, G. Sweers
  
• Limiting Sobolev inequalities and the 1-biharmonic operator. Adv. Nonlinear Anal. 3 (2014), suppl. 1, s19–s36
  E. Parini, B. Ruf, C. Tarsi
  
• Mock modular forms and class number relations. Math. Sci. (2014) 1: 6
  M.H. Mertens
  
• Morse-Bott inequalities in the presence of a compact Lie group action and applications. Differential Geom. Appl. 32 (2014), 68–87
  Wen Lu
  
• On the Fourier coefficients of meromorphic Jacobi forms. Int. J. Number Theory 10 (2014), no. 6, 1519–1540
  R. Olivetto
  
• On the Hamiltonian structure of the planar steady waterwave problem with vorticity. C. R. Math. Acad. Sci. Paris 352 (2014), no. 3, 205–211
  M.D. Groves, A. Stylianou
  
• Taut submanifolds and foliations. J. Differential Geom. 96 (2014), no. 3, 457–505
  S. Wiesendorf
  
• The eigenvalue problem for the 1-biharmonic operator. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13 (2014), no. 2, 307–332
  E. Parini, B. Ruf, C. Tarsi
  
• The fractional Cheeger problem. Interfaces Free Bound. 16 (2014), no. 3, 419–458
  L. Brasco, E. Lindgren, E. Parini
  
• The fundamental group of the space of contact structures on the 3-torus. Math. Res. Lett. 21 (2014), no. 6, 1257–1262
  H. Geiges, M. Klukas
  
• The metric anomaly of analytic torsion on manifolds with conical singularities. Comm. Partial Differential Equations 39 (2014), no. 1, 146–191
  W. Müller, Vertman
  
• Yamabe flow on manifolds with edges. Math. Nachr. 287 (2014), no. 2-3, 127–159
  E. Bahuaud, B. Vertman
  
• A note on inhomogeneous foliations with sections. Proc. Amer. Math. Soc. 143 (2015), no. 9, 4041–4043
  S. Wiesendorf
  
• Asymptotic formulae for partition ranks. Acta Arith. 168 (2015), no. 1, 83–100
  J. Dousse, M.H. Mertens
  
• Automorphic products of singular weight for simple lattices. Math. Z. 279 (2015), no. 1-2, 585–603
  M. Dittmann, H. Hagemeier, M. Schwagenscheidt
  
• Combinatorial quantum field theory and gluing formula for determinants. Lett. Math. Phys. 105 (2015), no. 3, 309–340
  N.B. Reshetikhin, B. Vertman
  
• Congruences for the Fourier coefficients of the Mathieu mock theta function. J. Number Theory 148 (2015), 451–462
  T. Miezaki, M. Waldherr
  
• Eigenvalue estimates of the spinc Dirac operator and harmonic forms on Kähler-Einstein manifolds. SIGMA Symmetry Integrability Geom. Methods Appl. 11 (2015)
  Nakad, Roger; M. Pilca
  
• Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems. Math. Z. 280 (2015), no. 3-4, 707– 732
  E. Parini, T. Weth
  
• Heat-trace asymptotics for edge Laplacians with algebraic boundary conditions. J. Anal. Math. 125 (2015), 285–318
  B. Vertman
  
• Mapping properties of the heat operator on edge manifolds. Math. Nachr. 288 (2015), no. 2-3, 126–157
  E. Bahuaud, E.B. Dryden, B. Vertman
  
• On the lifetime of conditioned Brownian motion in domains connected through small gaps, in Elliptic and Parabolic Equations, eds E. Schrohe e.a, Springer Proceedings in Mathematics & Statistics, Vol. 119 (2015) 77–109
  M. Erven, G. Sweers
  
• p-adic properties of modular shifted convolution Dirichlet series, Proc. AMS (2015)
  K. Bringmann, M.H. Mertens, K. Ono
  
• Pointwise behaviour of the solution of the Poisson problem near conical points. Nonlinear Anal. 121 (2015), 173–187
  M. Beygmohammad , G. Sweers
  
• Potential theory for the sum of the 1-Laplacian and p-Laplacian. Nonlinear Anal. 112 (2015), 165–180
  F. Krügel
  
• Regularizing infinite sums of zeta-determinants. Math. Ann. 361 (2015), no. 3-4, 835–862
  M. Lesch, B. Vertman
  
• Shape derivative of the Cheeger constant. ESAIM Control Optim. Calc. Var. 21 (2015), no. 2, 348–358
  E. Parini, N. Saintier
  
• Some properties of minimizers of a variational problem involving the total variation functional. Commun. Pure Appl. Anal. 14 (2015), no. 1, 341–360
  F. Krügel
  
• Special values for shifted convolution Dirichlet series, Mathematika (2015)
  M.H. Mertens, K. Ono
  
• The asymptotic profile of χy -genera of Hilbert schemes of points on K3 surfaces. Commun. Number Theory Phys. 9 (2015), no. 2, 413–436
  J. Manschot, J.M. Zapata Rolon
  
• The second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator. J. Geom. Anal. 25 (2015), no. 1, 25–63
  Wen Lu