Complex lines in tame almost complex tori

Antragsteller Professor Dr. Victor Bangert
Fachliche Zuordnung Mathematik
Förderung Förderung von 2002 bis 2007
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 5469304
 

Projektbeschreibung

In its geometric setting the Aubry-Mather Theory studies minimal geodesics in compact Riemannian manifolds, in particular in Riemannian tori. The present proposal aims at developing an analogous theory for holomorphic maps from the complex plane into a tame almost complex torus. These complex lines should generalize the affine complex lines in a standard complex torus. Although the nature of the differential equation and in particular the absence of a variational characterization of complex lines make the two problems very different there are some striking analogies: A KAM type perturbation result by J. Moser and global results by the proposer.
DFG-Verfahren Forschungsgruppen
Teilprojekt zu FOR 469:  Nonlinear Partial Differential Equations: Theoretical and Numerical Analysis