4 papers · 1 filter
Convex Floating Bodies of Equilibrium
D. I. Florentin, C. Schuett, E. M. Werner +1
We study a long standing open problem by Ulam, which is whether the Euclidean ball is the unique body of uniform density which will float in equilibrium in any direction. We answer…
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…