Gradient estimates for inverse curvature flows in hyperbolic space
Geometric Flows (2015)
- Volume: 1, Issue: 1, page 91-123
- ISSN: 2353-3382
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topJulian Scheuer. "Gradient estimates for inverse curvature flows in hyperbolic space." Geometric Flows 1.1 (2015): 91-123. <http://eudml.org/doc/275841>.
@article{JulianScheuer2015,
abstract = {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.},
author = {Julian Scheuer},
journal = {Geometric Flows},
keywords = {Curvature flows; Inverse curvature flows; Hyperbolic space; inverse curvature flows; hyperbolic space; long time existence; decay estimates; geodesic sphere},
language = {eng},
number = {1},
pages = {91-123},
title = {Gradient estimates for inverse curvature flows in hyperbolic space},
url = {http://eudml.org/doc/275841},
volume = {1},
year = {2015},
}
TY - JOUR
AU - Julian Scheuer
TI - Gradient estimates for inverse curvature flows in hyperbolic space
JO - Geometric Flows
PY - 2015
VL - 1
IS - 1
SP - 91
EP - 123
AB - 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.
LA - eng
KW - Curvature flows; Inverse curvature flows; Hyperbolic space; inverse curvature flows; hyperbolic space; long time existence; decay estimates; geodesic sphere
UR - http://eudml.org/doc/275841
ER -
References
top- [1] Claus Gerhardt. Closed Weingarten hypersurfaces in space forms. Geom. Anal. Calc. Var., pages 71–98, 1996. Zbl0932.35090
- [2] Claus Gerhardt. Curvature problems, volume 39 of Series in Geometry and Topology. International Press of Boston Inc., 2006. Zbl1131.53001
- [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]
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