In 2011, Lutwak, Yang and Zhang extended the definition of the Lp-Minkowski convex combination (p ≥ 1) from convex bodies containing the origin in their interiors to all measurable subsets in R n , and as a consequence, extended the Lp-Brunn-Minkowski inequality to the setting of all measurable sets. In this talk, I will present a functional extension of their Lp-Minkowski convex combination—the Lp,s–supremal convolution and the Lp-BMI for measurable sets to the class of Borel measures on R n having 1 s
-concave densities, with s ≥ 0; that is, for any pair of Borel sets A, B ⊂ R n , any t ∈ [0, 1] and p ≥ 1, one has µ((1 − t) ·p A +p t ·p B) p n+s ≥ (1 − t)µ(A) p n+s + tµ(B) p n+s , where µ is a measure on R n having a 1 s
-concave density. Moreover, the Lp-BMI for product measures with quasi-concave densities, Lp isoperimetric inequalities for general measures, etc, will also be provided under this new definition. This talk is based on a joint work with Dr. Michael Roysdon

Zoom ID: 939 3643 7199 (opens 15 min prior to the meeting)
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