Sharp Li-Yau-type gradient estimates on hyperbolic spaces

DOI10.1007/s12220-018-00133-8zbMath1435.58003arXiv1807.05710OpenAlexW2883572309WikidataQ128688597 ScholiaQ128688597MaRDI QIDQ2303782

Chengjie Yu, Feifei Zhao

Publication date: 5 March 2020

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.05710

zbMATH Keywords

heat equationheat kernelLi-Yau-type gradient estimate

Mathematics Subject Classification ID

Heat equation (35K05) Global Riemannian geometry, including pinching (53C20) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Ricci flows (53E20)

Related Items (8)

Hamilton type gradient estimates for a general type of nonlinear parabolic equations on Riemannian manifolds ⋮ Intrinsic dimensional functional inequalities on model spaces ⋮ Revisiting Li-Yau type inequalities on Riemannian manifolds ⋮ Sharp Li-Yau inequalities for Dunkl harmonic oscillators ⋮ Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency ⋮ Unnamed Item ⋮ Recurrence relations for heat kernels on spheres ⋮ Li-Yau multipLier set and optimal Li-Yau gradient estimate on hyperboLic spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Local Li-Yau's estimates on \(RCD^\ast(K,N)\) metric measure spaces
• Differential Harnack inequalities on Riemannian manifolds. I: Linear heat equation
• The Harnack estimate for the Ricci flow
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• On the parabolic kernel of the Schrödinger operator
• A matrix Harnack estimate for the heat equation
• Harnack inequalities on a manifold with positive or negative Ricci curvature
• Constrained and linear Harnack inequalities for parabolic equations
• The Li-Yau inequality and applications under a curvature-dimension condition
• Li-Yau gradient bounds on compact manifolds under nearly optimal curvature conditions
• Matrix Li-Yau-Hamilton estimates for the heat equation on Kähler manifolds
• On Harnack's inequalities for the Kähler-Ricci flow
• Harnack inequality for non-self-adjoint evolution equations
• On the Harnack inequalities of partial differential equations
• Li-Yau multipLier set and optimal Li-Yau gradient estimate on hyperboLic spaces
• Remarks on differential Harnack inequalities
• Li-Yau gradient bound for collapsing manifolds under integral curvature condition
• Sharp differential estimates of Li-Yau-Hamilton type for positive (p, p) forms on Kähler manifolds
• Heat Kernel Bounds on Hyperbolic Space and Kleinian Groups
• The Heat Kernel on Hyperbolic Space
• Uniqueness of Positive Solutions of the Heat Equation
• Generalized Li−Yau estimates and Huisken’s monotonicity formula

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