M. Alfonseca

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20132021

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math.MG2021

A solution to the Fifth and the Eighth Busemann-Petty problems in a small neighborhood of the Euclidean ball

M. Angeles Alfonseca, Fedor Nazarov, Dmitry Ryabogin +1

We show that the fifth and the eighth Busemann-Petty problems have positive solutions for bodies that are sufficiently close to the Euclidean ball in the Banach-Mazur distance.

math.MG2019

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…

math.MG2018

On bodies in $R^{5}$ with directly congruent projections or sections

M. Angeles Alfonseca, Michelle Cordier, Dmitry Ryabogin

Let $K$ and $L$ be two convex bodies in $R^{5}$ with countably many diameters, such that their projections onto all $4$ dimensional subspaces containing one fixed diameter…

math.MG2015

Counterexamples Related to Rotations of Shadows of Convex Bodies

M. Angeles Alfonseca, Michelle Cordier

We construct examples of two convex bodies $K, L$ in $R^{n}$ , such that every projection of $K$ onto a $(n - 1)$ -dimensional subspace can be rotated to be contained in the corr…

math.MG2013

An extension of a result by Lonke to intersection bodies

M. A. Alfonseca

In this paper we prove that intersection bodies cannot be direct sums using Fourier analytic techniques. This extends a result by Lonke. We also prove a necessary regularity condit…