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Geometric and Functional Analysis

, Volume 28, Issue 5, pp 1183–1208 | Cite as

Quermassintegral preserving curvature flow in Hyperbolic space

  • Ben AndrewsEmail author
  • Yong Wei
Article

Abstract

We consider the quermassintegral preserving flow of closed h-convex hypersurfaces in hyperbolic space with the speed given by any positive power of a smooth symmetric, strictly increasing, and homogeneous of degree one function f of the principal curvatures which is inverse concave and has dual f* approaching zero on the boundary of the positive cone. We prove that if the initial hypersurface is h-convex, then the solution of the flow becomes strictly h-convex for t > 0, the flow exists for all time and converges to a geodesic sphere exponentially in the smooth topology.

Keywords and phrases

Quermassintegral preserving flow Hyperbolic space Alexandrov reflection 

Mathematics Subject Classification

53C44 53C21 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia

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