# On a conjectural symmetric version of Ehrhard's inequality

@inproceedings{Livshyts2021OnAC, title={On a conjectural symmetric version of Ehrhard's inequality}, author={Galyna V. Livshyts}, year={2021} }

As one of the results of this manuscript, we show that for any logconcave measure μ on R, any pair of symmetric convex sets K and L, and any λ ∈ [0, 1], μ((1− λ)K + λL)n ≥ (1− λ)μ(K)n + λμ(L)n , where cn ≥ n−4−o(1). This constitutes progress towards the Dimensional BrunnMinkowski conjecture (see Gardner, Zvavitch [45], Colesanti, L, Marsiglietti [27]). Moreover, our bound improves for various special classes of log-concave measures. However, most of the paper is dedicated to studying sharp…

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