Isoperimetric inequalities for eigenvalues by inverse mean curvature flow

DOI10.1016/j.jmaa.2021.125438zbMath1475.53102arXiv1602.05290OpenAlexW3174511864MaRDI QIDQ2050902

Fangcheng Guo, Jiancheng Liu, Guang Han Li, Chuan Xi Wu

Publication date: 1 September 2021

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

Full work available at URL: https://arxiv.org/abs/1602.05290

zbMATH Keywords

monotonicityeigenvaluesinequalityinverse mean curvature flow

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Flows related to mean curvature (53E10)

Related Items (3)

Evolution of the first eigenvalue along the inverse mean curvature flow in space forms ⋮ First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The first eigenvalue of \(p\)-Laplace operator under powers of the \(m\)th mean curvature flow
• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• Isoperimetric upper bounds for the first eigenvalue
• Flow by mean curvature of convex surfaces into spheres
• Eigenvalues of \(\left(-\triangle + \frac{R}{2}\right)\) on manifolds with nonnegative curvature operator
• Flow of nonconvex hypersurfaces into spheres
• Forced convex mean curvature flow in Euclidean spaces
• Isoperimetric bounds for the first eigenvalue of the Laplacian
• Higher regularity of the inverse mean curvature flow
• The quermassintegral inequalities for \(k\)-convex starshaped domains
• A proof of the Faber-Krahn inequality for the first eigenvalue of the \(p\)-Laplacian
• Sharp upper bound for the first eigenvalue
• A geometric inequality on hypersurface in hyperbolic space
• Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space
• Hyperbolic Alexandrov-Fenchel quermassintegral inequalities. II
• First eigenvalues of geometric operators under the Ricci flow
• Monotonicity of the first eigenvalue of the Laplace and the p-Laplace operators under a forced mean curvature flow
• A Mean Curvature Type Flow in Space Forms
• Pinching estimates and motion of hypersurfaces by curvature functions

This page was built for publication: Isoperimetric inequalities for eigenvalues by inverse mean curvature flow