Surfaces expanding by non-concave curvature functions

DOI10.1007/s10455-018-9625-1zbMath1446.53077arXiv1609.00570OpenAlexW2518542059WikidataQ125879730 ScholiaQ125879730MaRDI QIDQ670316

Yong Wei, Haizhong Li, Xian Feng Wang

Publication date: 18 March 2019

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.00570

zbMATH Keywords

surfacesnon-concave curvature functionpinching ratio, space form

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Flows related to mean curvature (53E10)

Related Items

A class of inverse curvature flows and 𝐿^{𝑝} dual Christoffel-Minkowski problem ⋮ Contracting axially symmetric hypersurfaces by powers of the \(\sigma_k\)-curvature ⋮ Closed self-similar solutions to flows by negative powers of curvature ⋮ New pinching estimates for inverse curvature flows in space forms ⋮ Inverse curvature flows in Riemannian warped products ⋮ Shifted inverse curvature flows in hyperbolic space ⋮ Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces ⋮ Asymptotic convergence for a class of inverse mean curvature flows in ℝⁿ⁺¹ ⋮ A class of curvature flows expanded by support function and curvature function in the Euclidean space and hyperbolic space ⋮ Inverse curvature flows of rotation hypersurfaces ⋮ Curvature contraction flows in the sphere

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gradient estimates for inverse curvature flows in hyperbolic space
• Inverse curvature flows in hyperbolic space
• Inverse mean curvature flows in the hyperbolic 3-space revisited
• Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere
• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• Moving surfaces by non-concave curvature functions
• The inverse mean curvature flow in warped cylinders of non-positive radial curvature
• Flow by mean curvature of convex surfaces into spheres
• Flow of nonconvex hypersurfaces into spheres
• Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds
• Closed Weingarten hypersurfaces in Riemannian manifolds
• An expansion of convex hypersurfaces
• Contraction of convex hypersurfaces in Riemannian spaces
• Contraction of convex hypersurfaces in Euclidean space
• Inverse mean curvature flows in warped product manifolds
• Inverse mean curvature flow in quaternionic hyperbolic space
• Convex hypersurfaces with pinched second fundamental form
• Aleksandrov reflection and nonlinear evolution equations. I: The \(n\)-sphere and \(n\)-ball
• Convexity estimates for surfaces moving by curvature functions
• Non-scale-invariant inverse curvature flows in hyperbolic space
• Curvature flows in the sphere
• New pinching estimates for inverse curvature flows in space forms
• Inverse curvature flows in Riemannian warped products
• Non-scale-invariant inverse curvature flows in Euclidean space
• Surfaces expanding by the power of the Gauss curvature flow
• Curvature contraction flows in the sphere
• Surfaces expanding by the inverse Gauß curvature flow
• Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
• Pinching estimates and motion of hypersurfaces by curvature functions
• Analytic semigroups and optimal regularity in parabolic problems