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Isomorphic properties of Intersection bodies
A. Koldobsky, G. Paouris, M. Zymonopoulou
We study isomorphic properties of two generalizations of intersection bodies, the class of k-intersection bodies and the class of generalized k-intersection bodies. We also show th…
Stability of volume comparison for complex convex bodies
Alexander Koldobsky
We prove stability in the affirmative part of the Busemann-Petty problem on sections of complex convex bodies.
A hyperplane inequality for measures of convex bodies in
Alexander Koldobsky
We generalize the hyperplane inequality in dimensions up to 4 to the setting of arbitrary measures in place of the volume. To prove this generalization we establish stability in th…
Stability in the Busemann-Petty and Shephard problems
Alexander Koldobsky
A comparison problem for volumes of convex bodies asks whether inequalities for all imply that $\vol_n(K)\le \vol_n(L),$ where are convex bo…