Details
| Original language | English |
|---|---|
| Article number | 12 |
| Number of pages | 26 |
| Journal | Calculus of Variations and Partial Differential Equations |
| Volume | 62 |
| Issue number | 1 |
| Early online date | 5 Nov 2022 |
| Publication status | Published - Jan 2023 |
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.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Calculus of Variations and Partial Differential Equations, Vol. 62, No. 1, 12, 01.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Graphical mean curvature flow with bounded bi-Ricci curvature
AU - Assimos, Renan
AU - Savas-Halilaj, Andreas
AU - Smoczyk, Knut
N1 - Funding Information: The second author is supported by HFRI: Grant 133, and the third by DFG SM 78/7-1.
PY - 2023/1
Y1 - 2023/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85141173215&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2201.05523
DO - 10.48550/arXiv.2201.05523
M3 - Article
VL - 62
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 1
M1 - 12
ER -