Hyperbolic Alexandrov-Fenchel quermassintegral inequalities II

A Form of Alexandrov - Fenchel Inequalitypengfei Guan

Complex Hyperbolic Fenchel-nielsen Coordinates

Let Σ be a closed, orientable surface of genus g. It is known that the SU(2, 1) representation variety of π1(Σ) has 2g− 3 components of (real) dimension 16g− 16 and two components of dimension 8g−6. Of special interest are the totally loxodromic, faithful (that is quasi-Fuchsian) representations. In this paper we give global real analytic coordinates on a subset of the representation variety th...

The Quermassintegral Inequalities for Starshaped Domains

We give a simple proof of the insoperimetric inequality for quermassintegrals of non-convex starshaped domains, using a reslut of Gerhardt [6] and Urbas [13] on an expanding geometric curvature flow. The Alexandrov-Fenchel inequalities [1, 2] for the quermassintegrals of convex domains are fundamental in classical geometry. For a bounded domain Ω ⊂ Rn+1, we denote M = ∂Ω the boundary of Ω. We w...

Lp-Minkowski and Aleksandrov-Fenchel type inequalities

In this paper we establish the Lp-Minkowski inequality and Lp-Aleksandrov-Fenchel type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies, respectively. As applications, we get some related results. The paper new contributions that illustrate this duality of projection and intersection bodies will be presented. M.S.C. 2000: 52A40.

THE QUERMASSINTEGRAL INEQUALITIES FOR k-CONVEX STARSHAPED DOMAINS

We give a proof of the isoperimetric inequality for quermassintegrals of non-convex starshaped domains, using a result of Gerhardt [6] and Urbas [13] on an expanding geometric curvature flow. The Alexandrov-Fenchel inequalities [1, 2] for the quermassintegrals of convex domains are fundamental in classical geometry. For a bounded domain Ω ⊂ Rn+1, we denote M = ∂Ω the boundary of Ω. We will assu...