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An extension of Minkowski's theorem and its applications to questions about projections for measures
Galyna V. Livshyts
Minkowski's Theorem asserts that every centered measure on the sphere which is not concentrated on a great subsphere is the surface area measure of some convex body, and, moreover,…
Randomized coverings of a convex body with its homothetic copies, and illumination
Galyna Livshyts, Konstantin Tikhomirov
We present a probabilistic model of illuminating a convex body by independently distributed light sources. In addition to recovering C.A. Rogers' upper bounds for the illumination…
Maximal surface area of a convex set in with respect to exponential rotation invariant measures
Galyna Livshyts
Let be a positive number. Consider probability measure with density . We show that the maximal surface area of a convex body in $\math…
On the stability of Brunn-Minkowski type inequalities
Andrea Colesanti, Galyna V. Livshyts, Arnaud Marsiglietti
Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang \cite{BLYZ}, and it states that a certain strengthening of the classical Brunn-Minkowski inequali…