10 citations · 15 across the 6 of their papers we have counts for
6 papers · 1 filter
Sections and projections of nested convex bodies
I. González-García, J. Jerónimo-Castro, E. Morales-Amaya +1
One of the most important problems in Geometric Tomography is to establish properties of a given convex body if we know some properties over its sections or its projections. There…
Characterizations of the sphere by means of point-projections
J. Jeronimo_Castro, E. Morales-Amaya, D. J. Verdusco Hernández
In this work we prove the following: let be a convex body in the Euclidean space , , contained in the interior of the unit ball of , and le…
Helly type theorems for the sum of vectors in a normed plane
Imre Bárány, Jesús Jerónimo-Castro
The main results here are two Helly type theorems for the sum of (at most) unit vectors in a normed plane. Also, we give a new characterization of centrally symmetric convex sets i…
On a problem by Dol'nikov
Jesús Jerónimo-Castro, Alexander Magazinov, Pablo Soberón
In 2011 at an Oberwolfach workshop in Discrete Geometry, V. Dol'nikov posed the following problem. Consider three non-empty families of translates of a convex compact set in th…
The equal tangents property
J. Jeronimo-Castro, G. Ruiz-Hernandez, S. Tabachnikov
Let M be a smooth strictly convex closed surface in space and denote by H the set of points x in the exterior of M such that all the tangent segments from x to M have equal lengths…
Two characterizations of ellipsoidal cones
Jesús Jerónimo-Castro, Tyrrell B. McAllister
We give two characterizations of cones over ellipsoids. Let be a closed pointed convex linear cone in a finite-dimensional real vector space. We show that is a cone over an…