Article

Acta Mathematica Sinica, English Series

, Volume 29, Issue 4, pp 651-674

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

  • Chuan Qiang ChenAffiliated withSchool of Mathematical Sciences, University of Science and Technology of China Email author 
  • , Bo Wen HuAffiliated withDepartment of Mathematics and Applied Mathematics, Southwest University of Science and Technology

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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.

Keywords

Spacetime convexity microscopic convexity principle constant rank theorem parabolic convexity spacetime second fundamental form

MR(2010) Subject Classification

35K10 35B99