Estimations of the heat kernel on conic manifolds and applications

DOI10.1016/S0007-4497(00)00139-1zbMath0977.58024MaRDI QIDQ1588727

Hong-Quan Li

Publication date: 4 December 2000

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

zbMATH Keywords

heat kernelRiesz transformsconic Riemannian manifolds

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items

Bernstein inequalities via the heat semigroup, Restriction estimates in a conical singular space: wave equation, Gaussian heat kernel bounds through elliptic Moser iteration, Restriction estimates in a conical singular space: Schrödinger equation, The fractional porous medium equation on manifolds with conical singularities II, Heat kernel estimate in a conical singular space, Riesz transformations on a class of manifolds with conical singularities, Hölder continuity of the heat semigroup on conic manifolds, \(L_p\)-estimates of the wave equation on varieties with a conic singularity, Riesz transform on manifolds and heat kernel regularity, Gradient estimates for the heat semigroup on \(\mathbb H\)-type groups, Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg, Strichartz estimates and wave equation in a conic singular space

Cites Work

• Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds
• Spectral geometry of singular Riemannian spaces
• The fundamental solutions of the heat equations on Riemannian spaces with cone-like singular points
• The Riesz transformation on conical varieties
• Vector-valued multipliers on stratified groups
• On the wave equation on a compact Riemannian manifold without conjugate points
• Oscillating multipliers on Lie groups and Riemannian manifolds
• Inequalities for strongly singular convolution operators
• The Cauchy problem for systems in L\(_p\) and L\({_p,\alpha}\)
• On the diffraction of waves by conical singularities. I
• La transformation de Riesz sur les variétés coniques
• Riesz transforms for $1\le p\le 2$
• Riesz means on Lie groups and riemannian manifolds of nonnegative curvature
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item