Sharp Gaussian upper bounds for Schrödinger heat kernel on gradient shrinking Ricci solitons

DOI10.1007/s00229-022-01431-wzbMath1525.35162arXiv2006.13475OpenAlexW4303615205MaRDI QIDQ6050198

Jia-Yong Wu

Publication date: 12 October 2023

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.13475

zbMATH Keywords

sharp lower bounds for eigenvalues

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Schrödinger operator, Schrödinger equation (35J10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat kernel (35K08)

Cites Work

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• Heat kernel on smooth metric measure spaces and applications
• Remarks on non-compact gradient Ricci solitons
• A compactness theorem for complete Ricci shrinkers
• Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds
• On the Schrödinger equation and the eigenvalue problem
• Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution
• Uniformly elliptic operators on Riemannian manifolds
• Strong uniqueness of the Ricci flow
• Perelman's invariant, Ricci flow, and the Yamabe invariants of smooth manifolds
• Sharp logarithmic Sobolev inequalities on gradient solitons and applications
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Hardy-Littlewood theory for semigroups
• On the parabolic kernel of the Schrödinger operator
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• \(L^ p\) norms of non-critical Schrödinger semigroups
• Heat kernel bounds, conservation of probability and the Feller property
• Large time behavior of the heat kernel.
• An optimal parabolic estimate and its applications in prescribing scalar curvature on some open manifolds with Ricci \(\geq 0\)
• The Poisson kernel of positively curved manifolds
• Geometric inequalities for manifolds with Ricci curvature in the Kato class
• Heat kernel on Ricci shrinkers
• The Ricci Flow: Techniques and Applications
• On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
• A SHARP COMPARISON RESULT CONCERNING SCHRÖDINGER HEAT KERNELS
• Geometric Analysis
• Large time behavior of Schrödinger heat kernels and applications
• Global bounds of Schrödinger heat kernels with negative potentials