Constant rank theorems for Li-Yau-Hamilton type matrices of heat equations

DOI10.1090/PROC/16028zbMath1504.35100OpenAlexW4212794128WikidataQ122908838 ScholiaQ122908838MaRDI QIDQ5086932

Wei Zhang, Shujun Shi

Publication date: 8 July 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/16028

zbMATH Keywords

heat equationconstant rank theoremdifferential Harnack inequality

Mathematics Subject Classification ID

Heat equation (35K05) Maximum principles in context of PDEs (35B50) A priori estimates in context of PDEs (35B45) PDEs on manifolds (35R01)

Cites Work

• The Harnack estimate for the Ricci flow
• Convexity of solutions of semilinear elliptic equations
• On the parabolic kernel of the Schrödinger operator
• Convex solutions of certain elliptic equations have constant rank Hessians
• A matrix Harnack estimate for the heat equation
• Harnack inequalities for evolving hypersurfaces
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• Matrix Li-Yau-Hamilton estimates for the heat equation on Kähler manifolds
• Harnack estimate for the mean curvature flow
• A microscopic convexity principle for nonlinear partial differential equations
• A constant rank theorem for spacetime convex solutions of heat equation
• Harnack estimate for the \(H^{k}\)-flow
• Differential Harnack inequalities and the Ricci flow
• Harnack inequality for the negative power Gaussian curvature flow
• On Harnack's inequality and entropy for the gaussian curvature flow
• Harnack Estimate For Positive Solutions to a Nonlinear Equation Under Geometric Flow
• On Space-Time Quasiconcave Solutions of the Heat Equation

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