E. Morales-Amaya

activity

20202026

most citedSome results about equichordal convex bodies

3 citations · 13 across the 15 of their papers we have counts for

collaborators

15 papers

math.MG2026

A characterization of the ellipsoid in terms of pairs of sections associated by a harmonic homology

Efrén Morales-Amaya

Let $K$ be a convex body in an affine chart of the $n$ dimensional real Projective space $RP^{n}$ , $n \geq 3$ , let $H$ be a hyperplane which is not a support hyperplane of $…

math.MG2026

A characterization of the sphere in terms of the stereographic projection

Efrén Morales-Amaya

Let $K$ be a convex body in the 3-dimensional Euclidian space $E^{3}$ and let $N, S$ in the boubdary bd $K$ of $K$ , $N \neq = S$ . Suppose that the support plane $Π_{S}$ of $K$ at $…

math.MG2025

Convex bodies with sections with hyperplanes of symmetry

Efrén Morales-Amaya

Let $K \subset R^{n}$ be a convex body and let $p$ in the interior of $K$ , $n \geq 3$ . The point $p$ is said to be a \textit{Larman point} of $K$ if, for every hyperplane $Π…

math.MG2025

Characterizations of ellipsoids by means of the strong intersection property

E. Morales-Amaya

Let $E_{1}, E_{2} \subset R^{n}$ be two homothetic solid ellipsoids, $n \geq 3$ , with center at the origin $O$ of a system coordinates of $R^{n}$ , and $E_{1} \subset E_{2}$ . Then…

math.MG2024

A characterization of translated convex bodies

Efren Morales-Amaya

In this work we present a theorem regarding two convex bodies $K_{1}, K_{2} \subset R^{n}$ , $n \geq 3$ , and two families of sections of them, given by two families of tangent pl…

math.MG2024

Convex bodies with pairs of sections associated by reflections

Efren Morales-Amaya

In this work we prove that if for a pair of convex bodies $K_{1}, K_{2} \subset R^{n}$ , $n \geq 3$ , there exists a hyperplane $H$ and two distinct points $p_{1}$ and $p_{2}$ in $\ma…

math.MG2024★ 1 cited

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

Efrén Morales-Amaya, Geronimmo Mondragón, Jesús Jerónimo-Castro

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.MG2023

An equichordal characterization of the ellipsoid and the sphere

Victor A. Aguilar-Arteaga, Rafael Iván Ayala-Figueroa, Jesús Jerónimo-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.MG2023★ 1 cited

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

María Angeles Alfonseca, Michelle Cordier, Jesús Jerónimo-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 $Π$ passing through $p$ the se…

math.MG2023

Convex bodies with centrally symmetric sections

E. Morales-Amaya

Let $K \subset R^{n}$ be a convex body, $n \geq 3$ . We say that $K$ satisfies the Barker-Larman condition if there exists a ball $B$ in the interior of $K$ such that for every…

math.MG2021★ 3 cited

Some results about equichordal convex bodies

Jesús Jerónimo-Castro, Francisco G. Jimenez-Lopez, Efrén Morales-Amaya

Let $K$ and $L$ be two convex bodies in $R^{n}$ , $n \geq 2$ , with $L \subset int K$ . We say that $L$ is an equichordal body for $K$ if every chord of $K$ tangent to $L…

math.MG2021★ 3 cited

A characterization of centrally symmetric convex bodies in terms of visual cones

E. Morales-Amaya, J. Jerónimo-Castro, D. J. Verdusco-Hernández

In this work we prove the following result: Let $K$ be a strictly convex body in the Euclidean space $R^{n}, n \geq 3$ , and let $L$ be a hypersurface, which is the image of a…

math.MG2021★ 3 cited

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…

math.MG2021

Convex bodies with equipotential circles

Iván González-García, Jesús Jerónimo-Castro, Valentín Jiménez-Desantiago +1

Given a convex body $K \subset R^{2}$ we say that a circle $Ω \subset int K$ is an equipotential circle if every tangent line of $Ω$ cuts a chord $A B$ in $K$ such that…

math.MG2020★ 2 cited

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 $K$ be a convex body in the Euclidean space $R^{n}$ , $n \geq 3$ , contained in the interior of the unit ball of $R^{n}$ , and le…