کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4666983 1345432 2010 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Extremum problems for the cone volume functional of convex polytopes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Extremum problems for the cone volume functional of convex polytopes
چکیده انگلیسی

Lutwak, Yang and Zhang defined the cone volume functional U over convex polytopes in Rn containing the origin in their interiors, and conjectured that the greatest lower bound on the ratio of this centro-affine invariant U to volume V is attained by parallelotopes. In this paper, we give affirmative answers to the conjecture in R2 and R3. Some new sharp inequalities characterizing parallelotopes in Rn are established. Moreover, a simplified proof for the conjecture restricted to the class of origin-symmetric convex polytopes in Rn is provided.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 225, Issue 6, 20 December 2010, Pages 3214-3228