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On Space-Time Quasiconcave Solutions of the Heat Equation
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eBook
On Space-Time Quasiconcave Solutions of the Heat Equation
2019
Overview
In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time
quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly convexity results of the
spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain our ideas
and for completeness, we also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of
heat equation and for the second fundamental form of the convex level sets for harmonic function.
Publisher
American Mathematical Society
ISBN
9781470435240, 1470435241
