Curvature estimates for the level set of spatial quasiconcave solutions to a class of parabolic equations

Abstract

We prove a constant rank theorem for the second fundamental form of the spatial convex level surfaces of solutions to equations $u_t=F(\n^2u, \n u, u, t)$ under a structural condition, and give a geometric lower bound of the principal curvature of the spatial level surfaces.

22 pages

References in corpus (2)

• A Microscopic Convexity Principle for Nonlinear Partial Differential Equations
• Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations

Cited by in corpus (5)

• The Concavity of the Gaussian Curvature of the convex level sets of minimal surface with respect to the height
• Counterexamples to quasiconcavity for the heat equation
• On the microscopic spacetime convexity principle for fully nonlinear parabolic equations I: Spacetime convex solutions
• Strong space-time convexity and the heat equation
• Curvature estimates for the level sets of solutions of the Monge-Ampère equation $\det D^{2}u=1$