Refinement of Isoperimetric Inequality of Minkowski with the Account of Singularities in Boundaries of Intrinsic Parallel Bodies

V.I. Diskant
2014 Journal of Mathematical Physics, Analysis, Geometry  
The following inequalities are proved: where V (A), V (B) stand for the volumes of convex bodies A and B in R n (n ≥ 2), S(A, B) denotes the area of the surface of the body A relative to the body B, q is the capacity factor of the body B with respect to the body A, A i = A −ti (B) = A/(t i B) is the inner body parallel to the body A with respect to the body B at a distance t i , 0 = t 0 < t 1 < . . T 0 g(t)df (t) is the Riemann-Stieltjes integral of the function g(t) by the function f (t), and
more » ... unction f (t), and q 0 g(t)df (t) = lim T →q T 0 g(t)df (t).
doi:10.15407/mag10.03.309 fatcat:4c4wqoudcfbplgru33ltaqrdp4