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On Space-Time Quasiconcave Solutions of the Heat Equation (Memoirs of the American Mathematical Society)

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In this paper the authors 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, they 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 their ideas and for completeness, the authors 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.

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Format
paperback
Domain
Amazon UK
Release Date
30 June 2019
Listed Since
23 March 2019

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