Browsing by Subject "P sum"

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    On 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 Matemáticas
    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.