\(W\)-entropy, super Perelman Ricci flows, and \((K, m)\)-Ricci solitons
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Publication:2187710
DOI10.1007/s12220-019-00193-4zbMath1440.53113arXiv1706.07040OpenAlexW2963915811WikidataQ128013142 ScholiaQ128013142MaRDI QIDQ2187710
Publication date: 3 June 2020
Published in: The Journal of Geometric Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.07040
Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Ricci flows (53E20)
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Cites Work
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- On the classification of warped product Einstein metrics
- Perelman's entropy formula for the Witten Laplacian on Riemannian manifolds via Bakry-Emery Ricci curvature
- The \(W\)-entropy formula for the Witten Laplacian on manifolds with time dependent metrics and potentials
- Rigidity of quasi-Einstein metrics
- Differential Harnack inequalities on Riemannian manifolds. I: Linear heat equation
- Perelman's \(W\)-entropy for the Fokker-Planck equation over complete Riemannian manifolds
- Optimal transport and Perelman's reduced volume
- Comparison geometry for the Bakry-Emery Ricci tensor
- A logarithmic Sobolev form of the Li-Yau parabolic inequality
- Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds
- A matrix Harnack estimate for the heat equation
- Ricci solitons on compact three-manifolds
- Some geometric properties of the Bakry-Émery-Ricci tensor
- The entropy formula for linar heat equation
- On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows
- Hamilton differential Harnack inequality and \(W\)-entropy for Witten Laplacian on Riemannian manifolds
- Characterizations of the Ricci flow
- Addenda to ``The entropy formula for linear heat equation
- \(W\)-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds
- Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
- Ricci curvature for metric-measure spaces via optimal transport
- Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
- Ricci flow, entropy and optimal transportation
- Local gradient estimates of $p$-harmonic functions, $1/H$-flow, and an entropy formula
- New Examples of Complete Ricci Solitons
- Compact Einstein warped product spaces with nonpositive scalar curvature
- Hamilton's Harnack inequality and the \(W\)-entropy formula on complete Riemannian manifolds
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