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kinematic formulas of Total Mean Curvatures for Hypersurfaces

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Chinese Annals of Mathematics,Series B 2016年第1期37卷 137-148页

作者： Ming LI Jiazu ZHOU School of Mathematics and Statistics Chongqing University of Technology School of Mathematics and Statistics Southwest University College of Mathematical Science Kaili University

kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space

关键词： kinematic formula Total mean curvature Hypersurface

SOME DUAL kinematic formulaS

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Acta Mathematica Scientia 2007年第2期27卷 395-404页

作者：谢凤繁李德宜 School of Mathematics and Statistics Wuhan University College of Science Wuhan University of Science and Technology

In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals.

关键词： kinematic formula dual quermassintegrals chord power integral dual mixed volume star body convex body

The Willmore functional and the containment problem in R^4

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Science China Mathematics 2007年第3期50卷 325-333页

作者： Jia-zu ZHOU School of Mathematics and Statistics, Southwest University, Chongqing 400715, China Department of Mathematics, Polytechnic University, Brooklyn, NY 11201, USA School of Mathematics and Statistics Southwest University Chongqing China Department of Mathematics Polytechnic University Brooklyn USA

Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4.

关键词： mean curvature scalar curvature kinematic formula Minkowski quermassintegrals convex body convex hypersurface 52A22 53C65 51C16

The Bonnesen isoperimetric inequality in a surface of constant curvature

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Science China Mathematics 2012年第9期55卷 1913-1919页

作者： ZENG ChunNa MA Lei ZHOU JiaZu CHEN FangWeit School of Mathematics and Statistics Southwest University Chongqing 400715 China Gaozhou Normal College Guangdong University of Petrochemical Technology Maoming 525200 China Southeast Guizhou Vocational College of Technology for Nationalities Kaili 556000 China :Department of Mathematics and Statistics Guizhou College of Finance and Economics Guiyang 550004 China

We first estimate the containment measure of a convex domain to contain in another in a surface X of constant *** we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in *** we stren... 详细信息

关键词： hyperbolic plane projective plane kinematic formula Bonnesen isoperimetric inequality isoperi-metric deficit convex domain