Abstract The Lp-Brunn–Minkowski theory for p≥ 1, proposed by Firey and developed by
Lutwak in the 90's, replaces the Minkowski addition of convex sets by its Lp counterpart, in …

By using optimal mass transport theory we prove a sharp isoperimetric inequality in CD (0,
N) metric measure spaces assuming an asymptotic volume growth at infinity. Our result …

We interpret the log-Brunn–Minkowski conjecture of Böröczky–Lutwak–Yang–Zhang as a
spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert …

Let γ n be the standard Gaussian measure on R n. We prove that for every symmetric convex
sets K, L in R n and every λ∈(0, 1), γ n (λ K+(1− λ) L) 1 n⩾ λ γ n (K) 1 n+(1− λ) γ n (L) 1 n …

Abstract The Brunn-Minkowski theory in convex geometry concerns, among other things, the
volumes, mixed volumes, and surface area measures of convex bodies. We study …

We prove that the (B) conjecture and the Gardner–Zvavitch conjecture are true for all log-
concave measures that are rotationally invariant, extending previous results known for …

The Brunn-Minkowski Theory has seen several generalizations over the past century. Many
of the core ideas have been generalized to measures. With the goal of framing these …

We study several of the recent conjectures in regards to the role of symmetry in the
inequalities of Brunn–Minkowski type, such as the L_p L p-Brunn–Minkowski conjecture of …

The Local Logarithmic Brunn-Minkowski Inequality for Zonoids | SpringerLink Skip to main
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We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to $ n $
independent hyperplanes, and discuss the equality case and the uniqueness of the solution …