Complex lines in tame almost complex tori

• Applicant: Professor Dr. Victor Bangert
• Subject Area: Mathematics
• Term: from 2002 to 2007
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5469304

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 Programme: Research Units
• Subproject of: FOR 469: Nonlinear Partial Differential Equations: Theoretical and Numerical Analysis