Graphical mean curvature flow with bounded bi-Ricci curvature

authored by

Renan Assimos, Andreas Savas-Halilaj, Knut Smoczyk

Abstract

We consider the graphical mean curvature flow of strictly area decreasing maps f: M→ N, where M is a compact Riemannian manifold of dimension m> 1 and N a complete Riemannian surface of bounded geometry. We prove long-time existence of the flow and that the strictly area decreasing property is preserved, when the bi-Ricci curvature BRic

_M of M is bounded from below by the sectional curvature σ

_N of N. In addition, we obtain smooth convergence to a minimal map if Ric

_M≥ sup { 0 , sup

_Nσ

_N}. These results significantly improve known results on the graphical mean curvature flow in codimension 2.

Organisation(s)

Institut für Differentialgeometrie
Riemann Center for Geometry and Physics

External Organisation(s)

University of Ioannina

Type

Artikel

Journal

Calculus of Variations and Partial Differential Equations

Volume

62

No. of pages

26

ISSN

0944-2669

Publication date

01.2023

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Analysis, Angewandte Mathematik

Electronic version(s)

https://doi.org/10.48550/arXiv.2201.05523 (Access: Offen)
https://doi.org/10.1007/s00526-022-02369-3 (Access: Geschlossen)