The log-convex density conjecture and vertical surface area in warped products

DOI10.1515/advgeom-2015-0026zbMath1326.49077arXiv1107.4402OpenAlexW2963663744WikidataQ123113844 ScholiaQ123113844MaRDI QIDQ745248

Sean Howe

Publication date: 14 October 2015

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.4402

zbMATH Keywords

warped productproduct densityfiber manifoldsisoperimetric fiberslog-convex density conjecturestable spheres

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Optimization of shapes other than minimal surfaces (49Q10)

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Weighted isoperimetric inequalities in warped product manifolds ⋮ A Degenerate Isoperimetric Problem and Traveling Waves to a Bistable Hamiltonian System ⋮ Some isoperimetric inequalities in the plane with radial power weights ⋮ Approaching the isoperimetric problem in \(H_{\mathbb{C}}^m\) via the hyperbolic log-convex density conjecture ⋮ Weighted isoperimetric inequalities in cones and applications ⋮ A degenerate isoperimetric problem in the plane ⋮ Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities ⋮ Isoperimetric and stable sets for log-concave perturbations of Gaussian measures ⋮ Some isoperimetric inequalities on \(\mathbb{R}^N\) with respect to weights \(|x|^{\alpha}\) ⋮ The isoperimetric problem for a class of non-radial weights and applications ⋮ Isoperimetric symmetry breaking: a counterexample to a generalized form of the log-convex density conjecture ⋮ Some weighted isoperimetric problems on \({\mathbb{R}}^N_+\) with stable half balls have no solutions ⋮ On weighted isoperimetric inequalities with non-radial densities ⋮ A volume preserving flow and the isoperimetric problem in warped product spaces ⋮ Some isoperimetric inequalities with respect to monomial weights

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