Browsing by Subject "Borell Brascamp Lieb inequality"
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- PublicationOpen AccessBrunn-Minkowski type inequalities for the lattice point enumerator(Elsevier, 2020-08-26) Iglesias, David; Zvavitch, Artem ; Yepes Nicolás, Jesús; Matemáticas; Facultades de la UMU::Facultad de MatemáticasGeometric 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.
- PublicationOpen AccessOn discrete Lp Brunn–Minkowski type inequalities(Springer, 2022-08-11) Hernández Cifre, María de los Ángeles; Lucas Marín, Eduardo; Yepes Nicolás, Jesús; Matemáticas; Facultades de la UMU::Facultad de MatemáticasLp 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.