Integral Geometry And Convexity: Proceedings of the International Conference, Wuhan, China, 18 - 23 October 2004

by Grinberg, Eric L.; Li, Shougui; Zhang, Gaoyong; Zhou, Jiazu

• ISBN13: 9789812565136
• ISBN10: 9812565132
• Format: Hardcover
• Copyright: 2006-07-01
• Publisher: World Scientific Pub Co Inc

Summary

Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment. Remarkable advances have been made in several areas that involve the theory of convex bodies. This volume brings together contributions by leading international researchers in integral geometry, convex geometry, complex geometry, probability, statistics, and other convexity related branches. The articles cover both recent results and exciting directions for future research.

Table of Contents

Preface	v
Foreword	vii
Volume inequalities for sets associated with convex bodies	1	(16)
Stefano Campi and Paolo Gronchi
Integral geometry and Alesker's theory of valuations	17	(12)
Joseph H.G. Fu
Area and perimeter bisectors of planar convex sets	29	(8)
Paul Goodey
Radon Inversion: from lines to Grassmannians	37	(12)
Eric Grinberg
Valuations in the affine geometry of convex bodies	49	(18)
Monika Ludwig
Crofton measures in projective Finsler spaces	67	(32)
Rolf Schneider
Random methods in approximation of convex bodies	99	(8)
Carsten Schütt
Some generalized maximum principles and their applications to Chern type problems	107	(22)
Young Jin Suh
Floating bodies and illumination bodies	129	(12)
Elisabeth Werner
Applications of information theory to convex geometry	141	(12)
Deane Yang
Containment measures in integral geometry	153	(16)
Gaoyong Zhang and Jiazu Zhou
On the flag curvature and S-curvature in Finsler geometry	169	(8)
Xinyue Cheng
Double chord-power integrals of a convex body and their applications	177	(12)
Peng Xie and Jun Jiang
Lp dual Brunn-Minkowski type inequalities	189	(10)
Chang-jian Zhao and Gang-song Leng
On the relations of a convex set and its profile	199	(14)
Shougui Li and Yicheng Gong
Convex bodies with symmetric X-rays in two directions	213	(8)
Deyi Li and Ge Xiong
The kinematic measure of a random line segment of fixed length within a trapezoid	221
Fengfan Xie and Deyi Li