ISSN:
1420-8903
Keywords:
Primary 52A40
;
Secondary 52A30, 53A07
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For convex bodies inE d (d ≥ 3) with diameter 2 we consider inequalitiesW i − βW d−1 +(β - 1) W d ≤ 0 (i = 0, ⋯, d − 2) whereW j are the quermassintegrals. In addition, for a ball, equality is attained for a body of revolution for which the elementary symmetric functions d−1−i of main curvature radii is constant. The inequality is actually proved fori = d − 2 by means of Weierstrass's fundamental theorem of the calculus of variations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01840122
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