Gradient estimate for Schrödinger operators on manifolds

DOI10.1016/j.geomphys.2008.03.001zbMath1146.58018OpenAlexW2051325721MaRDI QIDQ938663

Qi-Hua Ruan

Publication date: 27 August 2008

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2008.03.001

zbMATH Keywords

Harnack inequalitySchrödinger operatorLiouville theoremgradient estimates

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (4)

Harnack differential inequalities for the parabolic equation \(u_t=\mathcal LF(u)\) on Riemannian manifolds and applications ⋮ Hamilton-type gradient estimates for a nonlinear parabolic equation on Riemannian manifolds ⋮ Gradient estimates for a nonlinear parabolic equation on complete smooth metric measure spaces ⋮ Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

Cites Work

• Unnamed Item
• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• On the parabolic kernel of the Schrödinger operator
• Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds
• A matrix Harnack estimate for the heat equation
• Harnack inequalities on a manifold with positive or negative Ricci curvature
• Harnack inequality for non-self-adjoint evolution equations
• On the Harnack inequalities of partial differential equations
• Logarithmic Sobolev Inequalities

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