Antonio Cañete

activity

20032024

most citedOn the isoperimetric problem in Euclidean space with density

1 citations · 1 across the 10 of their papers we have counts for

collaborators

14 papers

math.MG2024

Cheeger sets for rotationally symmetric planar convex bodies

Antonio Cañete

In this note we obtain some properties of the Cheeger set $C_{Ω}$ asociated to a $k$ -rotationally symmetric planar convex body $Ω$ . More precisely, we prove that $C_{Ω}$ is also $k$ -ro…

math.MG2023

Borsuk number for planar convex bodies

Antonio Cañete, Uwe Schnell

By using some simple tools from graph theory, we obtain a characterization of the planar convex bodies with Borsuk number equal to two. This result allows to give some examples of…

math.MG2023

Optimal divisions of a convex body

Antonio Cañete, Isabel Fernández, Alberto Márquez

For a convex body $C$ in $R^{d}$ and a division of $C$ into convex subsets $C_{1}, \dots, C_{n}$ , we can consider $ma x {F (C_{1}), \dots, F (C_{n})}$ (respectively, $min\{F(C_1),\ldot…

math.MG2019

On the isodiametric and isominwidth inequalities for planar bisections

Antonio Cañete, Bernardo González Merino

For a given planar convex compact set $K$ , consider a bisection ${A, B}$ of $K$ (i.e., $A \cup B = K$ and whose common boundary $A \cap B$ is an injective continuous curve connecting…

math.MG2018

Bisections of centrally symmetric planar convex bodies minimizing the maximum relative diameter

Antonio Cañete, Salvador Segura Gomis

In this paper we study the bisections of a centrally symmetric planar convex body which minimize the maximum relative diameter functional. We give necessary and sufficient conditio…

math.MG2015

The maximum relative diameter for multi-rotationally symmetric planar convex bodies

Antonio Cañete

In this work we study the maximum relative diameter functional $d_{M}$ in the class of multi-rotationally symmetric planar convex bodies. A given set $C$ of this class is $k$ -rotatio…