Strong space-time convexity and the heat equation
arXiv:1903.03208
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.
17 pages, v2 final version, with minor changes to appear in Indiana Univ. Math. J.; v3 a typo fixed