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

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

2010-06-24

arxiv.org/abs/1006.4787v3

Mathematics

Analysis of PDEs

22 pages

Scientific paper

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.

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