Publications at the Riemann Center
Graphical mean curvature flow with bounded bi-Ricci curvature
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.
Details
- Organisation(s)
-
Institute of Differential Geometry
Riemann Center for Geometry and Physics
- External Organisation(s)
-
University of Ioannina
- Type
- Article
- Journal
- Calculus of Variations and Partial Differential Equations
- Volume
- 62
- No. of pages
- 26
- ISSN
- 0944-2669
- Publication date
- 01.2023
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Analysis, Applied Mathematics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2201.05523 (Access:
Open
)
https://doi.org/10.1007/s00526-022-02369-3 (Access: Closed )
