Homotopy of area decreasing maps by mean curvature flow

authored by

Andreas Savas-Halilaj, Knut Smoczyk

Abstract

Let f : M → N be a smooth area decreasing map between two Riemannian manifolds (M, _gM) and (N, _gN). Under weak and natural assumptions on the curvatures of (M, _gM) and (N, _gN), we prove that the mean curvature flow provides a smooth homotopy of f to a constant map.

Organisation(s)

Institut für Differentialgeometrie
Riemann Center for Geometry and Physics

Type

Artikel

Journal

Advances in mathematics

Volume

255

Pages

455-473

No. of pages

19

ISSN

0001-8708

Publication date

01.04.2014

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Mathematik (insg.)

Electronic version(s)

https://doi.org/10.1016/j.aim.2014.01.014 (Access: Offen)