2 citations · 2 across the 6 of their papers we have counts for
9 papers
Self-dual sets up to a translation: a negative answer to Milman's question
Alex Segal
Let \(K,T\subset\mathbb R^n\) be convex bodies with the origin in their interiors. If \(K=T^\circ\), then the identity \( K+T=K^\circ+T^\circ \) holds trivially. V.~Milman asked wh…
The Scaled Polarity transform and related inequalities
Shoni Gilboa, Alexander Segal, Boaz A. Slomka
In this paper we deal with generalizations of the Mahler volume product for log-concave functions. We show that the polarity transform can be rescaled so that the Mahl…
On the Linear Structures Induced by the Four Order Isomorphisms Acting on
Dan I. Florentin, Alexander Segal
It is known that the volume functional satisfies certain concavity or convexity inequalities with respect to three of the four linear structures induced b…
A Santaló-type Inequality for the Transform
Dan I. Florentin, Alexander Segal
This paper deals with an analog of the Mahler volume product related to the transform acting in the class of geometric convex functions . We…
Functional Brunn-Minkowski Inequalities Induced by Polarity
Shiri Artstein-Avidan, Dan I. Florentin, Alexander Segal
We prove a new family of inequalities, which compare the integral of a geometric convolution of non-negative functions with the integrals of the original functions. For classical i…
Stability of Order Preserving Transforms
D. I. Florentin, A. Segal
The purpose of this paper is to show stability of order preserving/reversing transforms on the class of non-negative convex functions in , and its subclass, the clas…
Identifying Set Inclusion by Projective Positions and Mixed Volumes
D. I. Florentin, V. D. Milman, A. Segal
We study a few approaches to identify inclusion (up to a shift) between two convex bodies in . To this goal we use mixed volumes and fractional linear maps. We prove…
Stability and Rate of Convergence of the Steiner Symmetrization
D. I. Florentin, A. Segal
We present a direct analytic method towards an estimate for the rate of convergence (to the Euclidean Ball) of Steiner symmetrizations. To this end we present a modified version of…
Minkowski Symmetrizations of Star Shaped Sets
Dan Itzhak Florentin, Alexander Segal
We provide sharp upper bounds for the number of symmetrizations required to transform a star shaped set in arbitrarily close (in the Hausdorff metric) to the Euclid…