Selfsimilar solutions of the mean curvature flow

• Applicant: Professor Dr. Knut Smoczyk
• Subject Area: Mathematics
• Term: from 2005 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5453965

In this supplementary project concerned with selfsimilar solutions of the mean curvature flow we want to find additional classification results for selfsimilar submanifolds under various geometric conditions and to get a better understanding of what kind of constraints and obstructions for the existence of such submanifolds are necessary. We want to extend the results in the case of compact, selfsimilar submanifolds in the positive case, i.e. we want to pursue our research on shrinking solutions L. In particular, in the Lagrangian case there are promising results concerning the existence of a variant of the Futaki invariant in case of Lagrangian submanifolds which would eventually give us nice geometric informations on the topological nature of selfshrinking solutions L. We already obtained some constraints related to invariants, but so far these invariants are not fully understood and they are invariant on the Lagrangian cone instead of the Hamiltonian cone, which would be much more desirable. We believe that there are refinements of these invariants that are invariant on the Hamiltonian cone but not on the Lagrangian cone.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry