Dar’s conjecture and the log–Brunn–Minkowski inequality

90 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems (2017, methodology): “es (with respect to volume) starting from the works [33, 34] of Lutwak, Yang and Zhang. The Orlicz theory is in great demand (see e.g., [47] for some motivations) and is rapidly developing (see e.g., [4, 6, 19, 30, 42, 44, 45, 46, 53]). In particular, we establish the p-capacitary OrliczBrunn-Minkow”
Local $L^p$-Brunn-Minkowski inequalities for $p<1$ (2017, background): “Dar [17] was observed by Xi and Leng in [58].”
On the L dual Minkowski problem (2018, background): “, Böröczky, Lutwak, Yang & Zhang [9], Xi & Leng [64]), an inequality stronger than the classical Brunn-Minkowski inequality.”
Existence of solutions to the even dual Minkowski problem (2018, background): “The logarithmic Minkowski problem has strong connections with isotropic measures (Böröczky-LYZ [10]), curvature flows (Andrews [2, 3]), and the log-Brunn-Minkowski inequality (Böröczky-LYZ [8], Colesanti, Livshyts & Marsiglietti [15], Rotem [52], Saroglou [53], Xi & Leng [65]), an inequality stronge”
Local Lp-Brunn-Minkowski inequalities for p<1 (2017, background): “owski inequality for even log-concave measures were observed by Livshyts, Marsiglietti, P. Nayar and Zvavitch [47]. A surprising relation to a conjecture of S. Dar [17] was observed by Xi and Leng in [67]. 1.2 Main Results Our ﬁrst main result in this work conﬁrms the following local version of the ”