10 citations · 15 across the 6 of their papers we have counts for
7 papers
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…
Configuration spaces of plane polygons and a sub-Riemannian approach to the equitangent problem
J. Jeronimo-Castro, S. Tabachnikov
The equitangent locus of a convex plane curve consists of the points from which the two tangent segments to the curve have equal length. The equitangent problem concerns the relati…
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…