Gardner–Zvavitch dimensional Brunn–Minkowski conjecture

Let $cmu$ be an even log-concave measure on $cmathbb{R}^d$, let $clambdacin(0,1)$, and let $K,Lcsubsetcmathbb{R}^d$ be convex and centrally symmetric. Gardner–Zvavitch's dimensional Brunn–Minkowski conjecture. One has

$$cmu(clambda K+(1-clambda)L)^{1/d}cgeq clambda cmu(K)^{1/d}+(1-clambda)cmu(L)^{1/d}.$$

This generalizes the Gaussian Brunn–Minkowski inequality from Gaussian measure to all even log-concave measures. Partial results are known, but the conjecture remains open.