Publication: On discrete Lp Brunn–Minkowski type inequalities
Authors
Hernández Cifre, María de los Ángeles ; Lucas Marín, Eduardo ; Yepes Nicolás, Jesús
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Facultades de la UMU::Facultad de Matemáticas
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Publisher
Springer
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DOI
https://doi.org/10.1007/s13398-022-01309-2
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info:eu-repo/semantics/article
Description
Abstract
Lp Brunn–Minkowski type inequalities for the lattice point enumerator Gn(·) are shown, p ≥ 1, both in a geometrical and in a functional setting. In particular, we prove that Gn((1 − λ) · K +p λ · L + (−1, 1)^n)^{p/n} ≥ (1 −λ)Gn(K)^{p/n} + λGn(L)^{p/n} for any K, L ⊂ R^n bounded sets with integer points and all λ ∈ (0, 1). We also show that these new discrete analogues (for Gn(·)) imply the corresponding results concerning the Lebesgue measure.
Citation
Hernández Cifre, María A.; Lucas, Eduardo; Yepes Nicolás, Jesús. On discrete Lp Brunn-Minkowski type inequalities. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 116 (2022), no. 4, Paper No. 164, 14 pp.
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