Gradient estimates and Harnack inequalities for positive solutions of \(\mathfrak{L}u=\frac{\partial u}{\partial t}\) on self-shrinkers

DOI10.1007/S10114-019-8137-7zbMath1417.53047OpenAlexW2943925994MaRDI QIDQ2311740

Qing Chen, Yecheng Zhu

Publication date: 4 July 2019

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

Full work available at URL: https://doi.org/10.1007/s10114-019-8137-7

zbMATH Keywords

gradient estimateHarnack inequalityself-shrinker\(\infty\)-Bakry-Emery Ricci tensor

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (1)

Gradient estimate for the positive solutions of \(\mathcal{L} u=0\) and \(\mathcal{L}u = \frac{\partial u}{\partial t}\) on conformal solitons

Cites Work

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• The round sphere minimizes entropy among closed self-shrinkers
• Generic mean curvature flow. I: Generic singularities
• Smooth compactness of self-shrinkers
• Construction of complete embedded self-similar surfaces under mean curvature flow. III
• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• On the parabolic kernel of the Schrödinger operator
• Mean curvature self-shrinkers of high genus: non-compact examples
• Complete self-shrinkers confined into some regions of the space
• Computation of Self-Similar Solutions for Mean Curvature Flow
• Volume estimate about shrinkers
• Mean curvature flow
• Gaussian Harmonic Forms and two-dimensional self-shrinking surfaces
• ESTIMATES FOR EIGENVALUES OF $\mathfrak L$ OPERATOR ON SELF-SHRINKERS

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