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

DOI10.1007/s10114-012-1495-zzbMath1267.35105OpenAlexW1978826657MaRDI QIDQ1944844

Chuanqiang Chen, Bowen Hu

Publication date: 28 March 2013

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-012-1495-z

zbMATH Keywords

constant rank theoremparabolic convexityspacetime second fundamental form

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Maximum principles in context of PDEs (35B50) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (9)

On the microscopic spacetime convexity principle for fully nonlinear parabolic equations II: Spacetime quasiconcave solutions ⋮ Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank ⋮ Non-preservation of \(\alpha\)-concavity for the porous medium equation ⋮ Properties of solutions to a harmonic-mapping type equation with a Dirichlet boundary condition ⋮ On Space-Time Quasiconcave Solutions of the Heat Equation ⋮ On the microscopic spacetime convexity principle of fully nonlinear parabolic equations. I: Spacetime convex solutions ⋮ Strong space-time convexity and the heat equation ⋮ Convexity of level sets of minimal graph on space form with nonnegative curvature ⋮ Weak Harnack inequalities for eigenvalues and constant rank theorems

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