Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space
By Guofang Wang, Chao Xia. 2013
94 citations recorded by the source corpus.
In this paper, we solve various isoperimetric problems for the quermassintegrals and the curvature integrals in the hyperbolic space $\H^n$, by using quermassintegral preserving curvature flows. As a byproduct, we obtain hyperbolic Alexandrov-Fenchel inequalities.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/06ae5d71d787ddf7ce0a57364c5e93c3fa430150
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In Applied Mathematics
- Yong Wei
- Julian Scheuer
- M. Makowski
- Ben Andrews
- Xuzhong Chen
- S. Brendle
- Robert Haslhofer
- James A. McCoy
In Geometry and Topology
- Yong Wei
- Julian Scheuer
- M. Makowski
- Ben Andrews
- Xuzhong Chen
- S. Brendle
- Robert Haslhofer
- Bruce Kleiner
Citations in the corpus
- Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere (2013, methodology): “Wang and Xia used these results in [30] to obtain the Alexandrov-Fenchel inequalities for horospherically convex hypersurfaces in hyperbolic space.”
- Volume preserving flow and Alexandrov–Fenchel type inequalities in hyperbolic space (2018, methodology): “7 is not a homogeneous function of the principal curvatures κi and there are essential differences in the analysis compared with the previously mentioned work [10,25,32].”