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Efren Morales-Amaya

Publications and source records attributed to Efren Morales-Amaya.

3 recordsLinked to original sources
arXiv2025

Convex bodies with pairs of sections associated by reflections

In this work we prove that if for a pair of convex bodies $K_1, K_2 \subset \mathbb{R}^n$, $n \geq 3$, there exists a hyperplane $H$ and two distinct points $p_1$ and $p_2$ in $\mathbb{R}^n \setminus H$ such that for every $(n-2)$-plane $M \subset H$, there exists a reflection mapping the hypersection of $K_1$ defined by $\mathrm{aff}\{p_1, M\}$ onto the hypersection of $K_2$ defined by $\mathrm{aff}\{p_2, M\}$, then there exists a reflection which maps $K_1$ onto $K_2$.

math.MG↗
arXiv2025

A characterization of translated convex bodies

In this work we present a theorem regarding two convex bodies $K_1, K_2\subset \mathbb{R}^{n}$, $n\geq 3$, and two families of sections of them, given by two families of tangent planes of two spheres $S_i\subset \textrm{int}\textrm{ } K_i$, $i=1,2$ such that, for every pair $Π_1$, $Π_2$ of parallel supporting planes of $S_1$, $S_2$, respectively, which are corresponding (this means, that the outer normal vectors of the supporting half spaces determined by the two planes have the same direction), the sections $Π_1\cap K_1$, $Π_2\cap K_2$ are translated, the theorem claims that if $S_1$, $S_2$ have the same radius, the bodies are translated, otherwise, the bodies are also spheres.

math.MG↗