Affiliation:
1. Department of Mathematics Zhejiang University Hangzhou China
Abstract
AbstractIn this paper, we prove the following geometric inequalities in the Euclidean space , which are weighted Alexandrov–Fenchel type inequalities,
provided that is a star‐shaped and ‐convex hypersurface. Equality holds if and only if is a coordinate sphere in . As an application, by letting in the above inequality, we obtain a lower bound for the outer radius in terms of the curvature integrals for star‐shaped and ‐convex hypersurfaces.
Funder
National Key Research and Development Program of China
National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities
Reference28 articles.
1. Zur Theorie der gemischten Volumina von konvexen Körpern, II. Neue Ungleichungen zwischen den gemischten Volumina und ihre Anwendungen;Alexandrov A. D.;Mat. Sb. (N.S.),1937
2. Zur Theorie der gemischten Volumina von konvexen Körpern, III. Die Erweiterung zweeier Lehrsatze Minkowskis über die konvexen Polyeder auf beliebige konvexe Flachen;Alexandrov A. D.;Mat. Sb. (N.S.),1938
3. Some isoperimetric inequalities on RN with respect to weights |x|
4. A Minkowski Inequality for Hypersurfaces in the Anti-de Sitter-Schwarzschild Manifold
5. Sobolev and isoperimetric inequalities with monomial weights