Boundary regularity for mean curvature flows of higher codimension
In this paper, we derive global bounds for the Hölder norm of the gradient of solutions of graphic mean curvature flow with boundary of arbitrary codimension.
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Qi Ding
Works on minimal & CMC surfaces, homogeneous spaces and mean curvature flow.
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2017
Existence and non-existence of minimal graphs
We study the Dirichlet problem for minimal surface systems in arbitrary dimension and codimension via mean curvature flow, and obtain the existence of minimal graphs over arbitrary mean convex bounded domains for a large class of prescribed boundary data. This result can be seen as a natural generalization of the classical sharp criterion for solvability of the minimal surface equation by Jenkins-Serrin. In contrast, we also construct a class of prescribed boundary data on just mean convex domains for which the Dirichlet problem in codimension 2 is not solvable. Moreover, we study existence and the uniqueness of minimal graphs by perturbation.
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- Adrian Chun-Pong ChuShared topics: Minimal & CMC surfaces, Mean curvature flow
- Jiuzhou HuangShared topics: Minimal & CMC surfaces, Stability & uniqueness, Mean curvature flow
- Naoyuki KoikeShared topics: Minimal & CMC surfaces, Homogeneous spaces, Mean curvature flow
- Niels Martin MøllerShared topics: Minimal & CMC surfaces, Stability & uniqueness, Mean curvature flow
- César RosalesShared topics: Minimal & CMC surfaces, Stability & uniqueness, Mean curvature flow
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