Superconvexity of the Heat Kernel on Hyperbolic Space
Yongzhe Zhang
TL;DR
This paper proves a conjecture that the heat kernel on hyperbolic space exhibits superconvexity in all dimensions, enabling an extension of Huisken's monotonicity formula for mean curvature flow to hyperbolic spaces.
Contribution
It establishes the superconvexity of the heat kernel on hyperbolic space across all dimensions, confirming Bernstein's conjecture and extending geometric flow analysis.
Findings
Superconvexity of the heat kernel proven in all dimensions.
Extension of Huisken's monotonicity formula to hyperbolic space.
Validation of Bernstein's conjecture on heat kernel superconvexity.
Abstract
We prove a conjecture of Bernstein that the superconvexity of the heat kernel on hyperbolic space holds in all dimensions 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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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Mathematical Dynamics and Fractals