Superconvexity Of The Heat Kernel On Hyperbolic Space With Applications To Mean Curvature Flow

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY（2021）

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摘要

We prove a conjecture of Bernstein that the heat kernel on hyperbolic space of any dimension is supercovex in a suitable coordinate and, hence, there is an analog of Huisken's monotonicity formula for mean curvature flow in hyperbolic space of all dimensions.

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关键词

Superconvexity, heat kernel, hyperbolic space, mean curvature flow

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