Gradient estimates for inverse curvature flows in hyperbolic space

• Autorzy: Julian Scheuer
• Języki publikacji: EN

Abstrakty

EN

We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface.

Słowa kluczowe

EN

Curvature flows; Inverse curvature flows; Hyperbolic space

Kategorie tematyczne

• 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 35K55: Nonlinear parabolic equations

• Wydawca: De Gruyter Open
• Czasopismo: Geometric Flows
• Rocznik: 2015
• Tom: 1
• Numer: 1

Daty

otrzymano

2014-11-17

zaakceptowano

2014-12-10

online

2015-01-21

Twórcy

autor

Julian Scheuer

• Institut für Angewandte Mathematik, Universität Heidelberg

Bibliografia

• [1] Claus Gerhardt. Closed Weingarten hypersurfaces in space forms. Geom. Anal. Calc. Var., pages 71–98, 1996.
• [2] Claus Gerhardt. Curvature problems, volume 39 of Series in Geometry and Topology. International Press of Boston Inc., 2006.
• [3] Pei-Ken Hung and Mu Tao Wang. Inverse mean curvature flows in the hyperbolic 3-space revisited. Calc. Var. Partial Differential Equations, 2014. doi: 10.1007/s00526-014-0780-3. [Crossref][WoS]
• [4] Julian Scheuer. Non-scale-invariant inverse curvature flows in hyperbolic space. Calc. Var. Partial Differential Equations, 2014. doi: 10.1007/s00526-014-0742-9.[Crossref][WoS]

Identyfikatory

DOI

10.1515/geofl-2015-0002