Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space
Guofang Wang and Chao Xia
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Submission date: 18. Feb. 2014
published in: Advances in mathematics, 259 (2014), p. 532-556
DOI number (of the published article): 10.1016/j.aim.2014.01.024
MSC-Numbers: 52A40, 53C65, 53C44
Keywords and phrases: quermassintegral, curvature integral, isoperimetric problem, Alexandrov- Fenchel inequality
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In this paper, we solve various isoperimetric problems for the quermassintegrals and the curvature integrals in the hyperbolic space, by using quermassintegral preserving curvature ows. As a byproduct, we obtain hyperbolic Alexandrov-Fenchel inequalities.