Gradient Schrödinger operators, manifolds with density and applications

DOI10.1016/j.jmaa.2017.06.055zbMath1373.35104arXiv1209.6162OpenAlexW2963683329MaRDI QIDQ2014110

José M. Espinar

Publication date: 10 August 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.6162

zbMATH Keywords

manifolds with density\(\phi\)-parabolic manifoldsgradient Schrödinger operators

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (24)

Stability properties and gap theorem for complete \(f\)-minimal hypersurfaces ⋮ Uniqueness results and enclosure properties for hypersurfaces with boundary in weighted cylinders ⋮ The curve shortening problem associated to a density ⋮ Submanifolds with parallel weighted mean curvature vector in the Gaussian space ⋮ Mean convex properly embedded \([ \varphi , \vec{e}_3 \)-minimal surfaces in \(\mathbb{R}^3\)] ⋮ Two-sided hypersurfaces, entire Killing graphs and the mean curvature equation in warped products with density ⋮ On the space of \(f\)-minimal surfaces with bounded \(f\)-index in weighted smooth metric spaces ⋮ Rigidity and gap results for low index properly immersed self-shrinkers in \(\mathbb{R}^{m + 1}\) ⋮ Uniqueness of hypersurfaces in weighted product spaces via maximum principles for the drift Laplacian ⋮ Some maximum principles for the drift Laplacian applied to complete spacelike hypersurfaces ⋮ The global geometry of surfaces with prescribed mean curvature in ℝ³ ⋮ \(\lambda\)-Hypersurfaces on shrinking gradient Ricci solitons ⋮ Rigidity results and topology at infinity of translating solitons of the mean curvature flow ⋮ Height estimates for Killing graphs ⋮ Uniqueness of \(\phi\)-minimal hypersurfaces in warped product manifolds ⋮ Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities ⋮ Local rigidity, bifurcation, and stability of \(H_f\)-hypersurfaces in weighted Killing warped products ⋮ On the stability and parabolicity of complete \(f\)-minimal hypersurfaces in weighted warped products ⋮ Parabolicity criteria and characterization results for submanifolds of bounded mean curvature in model manifolds with weights ⋮ The rigidity and stability of complete 𝑓-minimal hypersurfaces in ℝⁿ×𝕊¹(𝕒) ⋮ Some integral formulae on weighted manifolds ⋮ Generalized Hsiung-Minkowski formulae on manifolds with density ⋮ Stability properties and topology at infinity of \(f\)-minimal hypersurfaces ⋮ On area comparison and rigidity involving the scalar curvature

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