Liouville theorems for the ancient solution of heat flows

DOI10.1090/S0002-9939-2011-11170-5zbMath1227.35108OpenAlexW1993200816WikidataQ125864294 ScholiaQ125864294MaRDI QIDQ3093436

Meng Wang

Publication date: 17 October 2011

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-11170-5

zbMATH Keywords

gradient estimatequasi-harmonic map

Mathematics Subject Classification ID

Heat equation (35K05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (6)

Liouville theorems for ancient solutions to the \(V\)-harmonic map heat flows ⋮ Differential Harnack inequalities for semilinear parabolic equations on Riemannian manifolds. II: Integral curvature condition ⋮ An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions ⋮ A Bernstein type theorem of ancient solutions to the mean curvature flow ⋮ Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry ⋮ Non-existence of eternal solutions to Lagrangian mean curvature flow with non-negative Ricci curvature

Cites Work

• Liouville theorems for self-similar solutions of heat flows
• On the parabolic kernel of the Schrödinger operator
• A matrix Harnack estimate for the heat equation
• The heat equation and harmonic maps of complete manifolds
• SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
• Differential equations on riemannian manifolds and their geometric applications

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