On the roots of the Wills functional

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:401

Article

Hernandez Cifre, Maria A.¹  Yepes Nicolas, Jesus¹ 

[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

关键词: Wills functional;    Location of roots;    Successive minima;    Inradius;    Circumradius;    Steiner polynomial;   

DOI  :  10.1016/j.jmaa.2012.12.065

来源: Elsevier

【 摘 要 】

We investigate the roots of Wills polynomials of convex bodies. We study the structure, showing that the set of roots in the upper half plane is a convex cone, monotonous with respect to the dimension. In particular, we give its precise description for dimensions n = 2, 3. We also show that for n <= 7 this cone is completely contained in the (open) left half plane, which is not true in dimensions >= 14. Moreover, we study the size of the roots of the Wills polynomial, bounding them in terms of functionals like the in- and circumradius of the set. We also relate the roots of the Steiner and the Wills polynomials. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free