Functionals on the Spaces of Convex Bodies  

作　　者：Chuanming ZONG 

机构地区：[1]School of Mathematical Sciences, Peking University

出　　处：《Acta Mathematica Sinica,English Series》2016年第1期124-136,共13页数学学报（英文版）

基　　金：Supported by 973 Programs(Grant Nos.2013CB834201 and 2011CB302401);the National Science Foundation of China(Grant No.11071003);the Chang Jiang Scholars Program of China

摘　　要：In geometry, there are several challenging problems studying numbers associated to convex bodies. For example, the packing density problem, the kissing number problem, the covering density problem, the packing-covering constant problem, Hadwiger＇s covering conjecture and Borsuk＇s partition conjecture. They are flmdamental and fascinating problems about the same objects. However, up to now, both the methodology and the technique applied to them are essentially different. Therefore, a common foundation for them has been much expected. By treating problems of these types as functionals defined on the spaces of n-dimensional convex bodies, this paper tries to create such a foundation. In particular, supderivatives for these functionals will be studied.In geometry, there are several challenging problems studying numbers associated to convex bodies. For example, the packing density problem, the kissing number problem, the covering density problem, the packing-covering constant problem, Hadwiger＇s covering conjecture and Borsuk＇s partition conjecture. They are flmdamental and fascinating problems about the same objects. However, up to now, both the methodology and the technique applied to them are essentially different. Therefore, a common foundation for them has been much expected. By treating problems of these types as functionals defined on the spaces of n-dimensional convex bodies, this paper tries to create such a foundation. In particular, supderivatives for these functionals will be studied.

关 键 词：Packing density covering density kissing number Hadwiger＇s conjecture 

分 类 号：O186.5[理学—数学]