Translating Solutions of the Nonparametric Mean Curvature Flow with Nonzero Neumann Boundary Data in Product Manifold Mn × R*

Citation:

Deliang XU,Ya GAO,Yi-Juan GONG.Translating Solutions of the Nonparametric Mean Curvature Flow with Nonzero Neumann Boundary Data in Product Manifold Mn × R*[J].Chinese Annals of Mathematics B,2022,43(4):601~620
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Authors:

Deliang XU; Ya GAO;Yi-Juan GONG

Foundation:

National Natural Science Foundation of China (Nos. 11801496,11926352), the Fok Ying-Tung Education Foundation (China) and Hubei Key Laboratory of Applied Mathematics (Hubei University).
Abstract: In this paper, the authors can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold Mn × R, where Mn is an n-dimensional (n ≥ 2) complete Riemannian manifold with nonnegative Ricci curvature, and R is the Euclidean 1-space.

Keywords:

Translating solutions, Singularity, Nonparametric mean curvature flow,Convexity, Ricci curvature.

Classification:

53C42, 53B20, 35B50, 35K93
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