Differentiability properties of the family of p-parallel bodies

Applicable Analysis and Discrete Mathematics

article

Maria A. Hernández Cifre¹  Antonio R. Martínez Fernández¹  Eugenia Saorín Gómez² 

[1] Universidad de Murcia Spain;Otto-von-Guericke Universit¨at Magdeburg Germany

关键词: p-difference of convex bodies;    (mixed) quermassintegral;    differentiability;    relative inradius;    (+p-) concave family;   

DOI  :  10.2298/AADM160325005C

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

We investigate the differentiability of the quermassintegrals with respect tothe one-parameter family of the p-parallel bodies. As in the classical case, weobtain that the volume is always differentiable. Although there is no polynomial expression for a p-sum, the rest of quermassintegrals are differentiableon positive values of the parameter too. We prove a sharp lower bound forthe derivative of the support function of the p-inner parallel bodies alongwith equality conditions.

【 授权许可】

Unknown