Codimension two mean curvature flow of entire graphs

authored by

Andreas Savas Halilaj, Knut Smoczyk

Abstract

We consider the graphical mean curvature flow of maps (Formula presented.), (Formula presented.), and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well-known maximum principle of Ecker and Huisken derived in their seminal paper [Ann. of Math. (2) 130:3(1989), 453–471]. In the case of uniformly area decreasing maps (Formula presented.), (Formula presented.), we use this maximum principle to show that the graphicality and the area decreasing property are preserved. Moreover, if the initial graph is asymptotically conical at infinity, we prove that the normalized mean curvature flow smoothly converges to a self-expander.

Organisation(s)

Institut für Differentialgeometrie
Riemann Center for Geometry and Physics

External Organisation(s)

University of Ioannina

Type

Artikel

Journal

Journal of the London Mathematical Society

Volume

110

No. of pages

33

ISSN

0024-6107

Publication date

10.10.2024

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Allgemeine Mathematik

Electronic version(s)

https://doi.org/10.48550/arXiv.2403.10739 (Access: Offen)
https://doi.org/10.1112/jlms.13000 (Access: Offen)