Improvements of the analogy isoperimetric inequality and the theorem of stability of its extremal solution - Diskant, V. I. (Журнал математичної фізики, аналізу, геометрії, 2005)
The following inequality is proved:V^n/(n-m)_m(A,B)-V^m/(n-m)(B)V(A)(V^1/(n-m)_m(A,B)- ρ V^1/(n-m)(B))^n - V^m/(n-m)(B)V(A_-ρ(B)), 0ρq,his consequents and the theorem of stability of solution X equation V^n_m(X,B)-V^m(B)V^n-m(X)=0 at V(X)=V(B). In given inequality V(A), V(B) – the volumes of convex bodies A and B in R^n n2, V_m(A,B) – m-mixed volume of bodies A and B, 1mn-1, q – a capacity coeficient of B in a body A, A_-ρ(B)) – internal body which is parallel to body A relatively to B with coeficient ρ. Mathematical Subject Classification: 52A38, 52A40.