Jes'us Jer'onimo-Castro

activity

20242026

collaborators

5 papers

math.MG2026

An equichordal characterization of the ellipsoid and the sphere

Victor A. Aguilar-Arteaga, Rafael IvÃ¡n Ayala-Figueroa, JesÃºs JerÃ³nimo-Castro +1

Let $K$ and $L$ be two convex bodies in $R^{n}$ , $n \geq 3$ , with $L \subset int K$ . In this paper we prove the following result: if every two parallel chords of $K$ ,…

math.MG2025

Flat grazes of convex bodies and local characterization of quadrics

JesÃºs JerÃ³nimo-Castro, Luis Montejano, EfrÃ©n Morales-Amaya

We prove several localized characterizations of quadrics and, between them, the localized Blaschke's Theorem and use this result to give some characterizations of the ellipsoid rel…

math.MG2025

A Characterization of the sphere and a body of revolution by means of Larman points

MarÃa Angeles Alfonseca, Michelle Cordier, JesÃºs JerÃ³nimo-Castro +1

Let $K \subset R^{n}$ , $n \geq 3$ , be a convex body. A point $p$ the interior of $K$ is said to be a Larman point of $K$ if for every hyperplane $I^$ passing through $p$ the s…

math.MG2025

On characteristic properties of the ellipsoid in terms of circumscribed cones of a convex body

We strongly believe that in order to prove two important geometrical pro\-blems in convexity, namely, the G. Bianchi and P. Gruber's Conjecture \cite{bigru} and the J. A. Barker an…

math.MG2024

Ball characterizations in planes and spaces of constant curvature, I

JesÃºs JerÃ³nimo-Castro, Endre Makai

Let us have in S^2, R^2 or H^2 a pair of convex bodies, for S^2 different from S^2, such that the intersections of any congruent copies of them are centrally symmetric. Then our bo…