Spectral bounds for the torsion function

DOI10.1007/S00020-017-2371-0zbMath1378.58024arXiv1701.02172OpenAlexW2578885660WikidataQ59614129 ScholiaQ59614129MaRDI QIDQ1677090

Peng Zhang

Publication date: 10 November 2017

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.02172

zbMATH Keywords

Riemannian manifoldDirichlet Laplaciannon-negative Ricci curvaturetorsion function

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Boundary value problems on manifolds (58J32) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (12)

Intrinsic ultracontractivity for domains in negatively curved manifolds ⋮ Bounds for exit times of Brownian motion and the first Dirichlet eigenvalue for the Laplacian ⋮ On two functionals involving the maximum of the torsion function ⋮ On a Pólya functional for rhombi, isosceles triangles, and thinning convex sets ⋮ On the \({ L}^{ p}\) norm of the torsion function ⋮ Localization and landscape functions on quantum graphs ⋮ Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle ⋮ \(L_\infty\)-estimates for the torsion function and \(L_{\infty}\)-growth of semigroups satisfying Gaussian bounds ⋮ Conformal Skorokhod embeddings and related extremal problems ⋮ On efficiency and localisation for the torsion function ⋮ On relations between principal eigenvalue and torsional rigidity ⋮ Spectral upper bound for the torsion function of symmetric stable processes

Cites Work

• Estimates for the torsion function and Sobolev constants
• On Pólya's inequality for torsional rigidity and first Dirichlet eigenvalue
• Analysis of the Laplacian on a complete Riemannian manifold
• On the parabolic kernel of the Schrödinger operator
• \(L_\infty\)-estimates for the torsion function and \(L_{\infty}\)-growth of semigroups satisfying Gaussian bounds
• Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Hardy inequality and L ^p estimates for the torsion function
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