Complex lines in tame almost complex tori.

In its geometric setting 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.

Additional information: http://home.mathematik.uni-freiburg.de/fg/projects/B1/
contact person: Prof. Dr. Victor Bangert
Phone: 0761/203-5562
Email: bangert@email.mathematik.uni-freiburg.de

Start of project: 01.02.2003
End of project: 31.01.2007

Albert-Ludwigs-University Freiburg
Prof. Dr. Victor Bangert
Abteilung für Reine Mathematik
Prof. Dr. Victor Bangert
Eckerstraße 1
79104 Freiburg
Germany

Phone: +49 761 203-5562
Fax: +49 761 203-5541
Email: bangert@email.mathematik.uni-freiburg.de
http://home.mathematik.uni-freiburg.de/geometrie/bangert/
Actual Research Report