Publication: Brunn-Minkowski type inequalities for the lattice point enumerator
Authors
Iglesias, David ; Zvavitch, Artem ; Yepes Nicolás, Jesús
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Facultades de la UMU::Facultad de Matemáticas
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Publisher
Elsevier
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DOI
https://doi.org/10.1016/j.aim.2020.107193.
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info:eu-repo/semantics/article
Description
Abstract
Geometric and functional Brunn-Minkowski type inequalities for the lattice point enumerator Gn(⋅) are provided. In particular, we show that Gn((1−λ)K+λL+(−1,1)^n)^{1/n}≥(1−λ)Gn(K)^{1/n}+λGn(L)^{1/n} for any non-empty bounded sets K,L⊂R^n and all λ∈(0,1). We also show that these new discrete versions imply the classical results, and discuss some links with other related inequalities.
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Citation
David Iglesias, Jesús Yepes Nicolás, Artem Zvavitch, Brunn-Minkowski type inequalities for the lattice point enumerator, Advances in Mathematics, Volume 370, 2020
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