Strong space-time convexity and the heat equation
Albert Chau, Ben Weinkove
TL;DR
This paper proves local strong convexity of space-time level sets of the heat equation on convex rings with zero initial data, using a novel parabolic two-point maximum principle.
Contribution
It introduces a parabolic two-point maximum principle to establish strong convexity of heat equation level sets, extending Borell's earlier results.
Findings
Proves local strong convexity of space-time level sets
Introduces a parabolic two-point maximum principle
Strengthens previous convexity results for the heat equation
Abstract
We prove local strong convexity of the space-time level sets of the heat equation on convex rings for zero initial data, strengthening a result of Borell. Our proof introduces a parabolic version of a two-point maximum principle of Rosay-Rudin.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Advanced Topology and Set Theory