Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency

DOI10.1007/s00526-024-02668-xarXiv2306.10143OpenAlexW4392163918MaRDI QIDQ6190031

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Publication date: 5 March 2024

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.10143

Mathematics Subject Classification ID

Heat equation (35K05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Ricci flows (53E20)

Cites Work

• An upper bound for Hessian matrices of positive solutions of heat equations
• Three circles theorems for harmonic functions
• On the distributional Hessian of the distance function
• Differential Harnack inequalities on Riemannian manifolds. I: Linear heat equation
• The conjugate heat equation and ancient solutions of the Ricci flow
• The Harnack estimate for the Ricci flow
• A matrix Li-Yau-Hamilton estimate for Kähler-Ricci flow
• A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow
• Differential Harnack estimates for backward heat equations with potentials under the Ricci flow
• Gradient estimates for the heat equation under the Ricci flow
• Gradient estimates for solutions of the heat equation under Ricci flow
• On the parabolic kernel of the Schrödinger operator
• Four-manifolds with positive curvature operator
• Partial differential equations. 4th ed
• A matrix Harnack estimate for the heat equation
• Harmonic functions on manifolds
• Constrained and linear Harnack inequalities for parabolic equations
• Harmonic functions with polynomial growth
• The entropy formula for linar heat equation
• The fundamental solution on manifolds with time-dependent metrics
• Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure
• Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture
• Li-Yau gradient bounds on compact manifolds under nearly optimal curvature conditions
• Addenda to ``The entropy formula for linear heat equation
• Matrix Li-Yau-Hamilton estimates for the heat equation on Kähler manifolds
• On Harnack's inequalities for the Kähler-Ricci flow
• Three-manifolds with positive Ricci curvature
• Li-Yau multipLier set and optimal Li-Yau gradient estimate on hyperboLic spaces
• Li-Yau inequalities in geometric analysis
• Kähler-Ricci shrinkers and ancient solutions with nonnegative orthogonal bisectional curvature
• Sharp Li-Yau-type gradient estimates on hyperbolic spaces
• Parabolic frequency monotonicity on compact manifolds
• Constrained matrix Li-Yau-Hamilton estimates on Kähler manifolds
• A generalization of Hamilton's differential Harnack inequality for the Ricci flow
• Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature
• The Ricci flow under almost non-negative curvature conditions
• Differential Harnack estimates for time-dependent heat equations with potentials
• The effect of curvature on convexity properties of harmonic functions and eigenfunctions
• Li-Yau gradient bound for collapsing manifolds under integral curvature condition
• Manifolds with 1/4-pinched curvature are space forms
• A uniqueness theorem for parabolic equations
• Nodal sets of solutions of elliptic and parabolic equations
• SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
• Local and global analysis of eigenfunctions
• Unique continuation for elliptic operators: A geometric-variational approach
• Carleman Estimates, Optimal Three Cylinder Inequality, and Unique Continuation Properties for Solutions to Parabolic Equations
• Qnique Continuation for
• Parabolic Frequency on Manifolds
• Hamilton’s gradient estimate for the heat kernel on complete manifolds
• A harnack inequality for parabolic differential equations
• A note on parabolic frequency and a theorem of Hardy–Pólya–Szegö
• Geometric Analysis
• Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons
• Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
• Parabolic Frequency on Ricci Flows
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