, Volume 29, Issue 4, pp 651-674
Date: 08 Nov 2012

A microscopic convexity principle for spacetime convex solutions of fully nonlinear parabolic equations

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Abstract

We study microscopic spacetime convexity properties of fully nonlinear parabolic partial differential equations. Under certain general structure condition, we establish a constant rank theorem for the spacetime convex solutions of fully nonlinear parabolic equations. At last, we consider the parabolic convexity of solutions to parabolic equations and the convexity of the spacetime second fundamental form of geometric flows.

The first author is supported by National Natural Science Foundation of China (Grant No. 10871187)