Uniform Sobolev Resolvent Estimates for the Laplace–Beltrami Operator on Compact Manifolds

DOI10.1093/imrn/rnt051zbMath1297.35256arXiv1209.5689OpenAlexW2141556079MaRDI QIDQ2878734

Peng Shao, Xiao Hua Yao

Publication date: 5 September 2014

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.5689

zbMATH Keywords

Laplace-Beltrami operatorcompact manifoldsuniform Sobolev resolvent estimates

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Elliptic equations on manifolds, general theory (58J05) PDEs on manifolds (35R01)

Related Items (12)

Uniform Sobolev estimates on compact manifolds involving singular potentials ⋮ Remarks on \(L^{p}\)-limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems ⋮ Uniform resolvent estimates for Laplace-Beltrami operator on the flat Euclidean cone ⋮ Concerning \(L^p\) resolvent estimates for simply connected manifolds of constant curvature ⋮ Resolvent estimates for Schrödinger operators with potentials in Lebesgue spaces ⋮ Sharp resolvent estimates outside of the uniform boundedness range ⋮ Spectral cluster estimates for Schrödinger operators of relativistic type ⋮ Endpoint resolvent estimates for compact Riemannian manifolds ⋮ Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentials ⋮ Uniform resolvent estimates on manifolds of bounded curvature ⋮ Uniform Sobolev estimates in \(\mathbb{R}^n\) involving singular potentials ⋮ (Lr,Ls) Resolvent estimate for the sphere off the line 1 r −1 s = 2 n

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