5 papers
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…
Uniqueness Results for Bodies of Constant Width in the Hyperbolic Plane
M. Angeles Alfonseca, Michelle Cordier, Dan I. Florentin
Following Santaló's approach, we prove several characterizations of a disc among bodies of constant width, constant projections lengths, or constant section lengths on given famili…
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…