Publication: On discrete Brunn-Minkowski and isoperimetric type inequalities
Authors
Iglesias López, David ; Lucas Marín, Eduardo ; Yepes Nicolás, Jesús
item.page.secondaryauthor
item.page.director
Publisher
Elsevier
publication.page.editor
publication.page.department
DOI
https://doi.org/10.1016/j.disc.2021.112640
item.page.type
info:eu-repo/semantics/article
Description
Abstract
We show that the lattice point enumerator Gn(·) satisfies G tK + sL + (−1,[t + s])n 1/n ≥ tG (K)1/n + sG (L)1/n
for any K, L ⊂ Rn bounded sets with integer points and all t, s ≥ 0.
We also prove that a certain family of compact sets, extending that of cubes [−m, m]n, with m ∈ N, minimizes the functional Gn(K + t[−1, 1]n), for any t ≥ 0, among those bounded sets K ⊂ Rn with given positive lattice point enumerator.
Finally, we show that these new discrete inequalities imply the cor- responding classical Brunn-Minkowski and isoperimetric inequalities for non-empty compact sets.
publication.page.subject
Citation
Discrete Mathematics
Volume 345, Issue 1, January 2022, 112640
item.page.embargo
Collections
Ir a Estadísticas
Este ítem está sujeto a una licencia Creative Commons. http://creativecommons.org/licenses/by-nc-nd/4.0/