The log-Brunn-Minkowski inequality

By K. Boroczky, Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2012

374 citations recorded by the source corpus.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/4d04bdea1b23912b30c356d055c45f1e68d49ea0

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Citations in the corpus

Local Lp-Brunn-Minkowski inequalities for p<1 (2017, methodology): “ures µ, a novel necessary and suﬃcient subspace concentration condition ensuring the existence question was obtained by B¨oro¨czky–Lutwak–Yang–Zhang in [7], and the uniqueness question was settled in [6] in dimension n = 2; it remains open in full generality in dimension n ≥ 3. In Theorem 11.2, we t”
On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities (2015, methodology): “In [28] the proof is done by linking the problem to the new log-Brunn-Minkowski inequality of Böröczky, Lutwak, Yang and Zhang, see [5], [6], [27] and [28].”
On the planar dual Minkowski problem (2018, methodology): “This is because the equation describes the self-similar solution of curve shortening flow, and by Gage-Hamilton’s Theorem [23] it must be a circle; see also [5, 9, 24, 32].”
More on logarithmic sums of convex bodies (2014, background): “The following is conjectured in [4] (without the equality cases): 1”
Cone-volume measure of general centered convex bodies (2016, neutral): “Zhang [10,11], M.”
Dar’s conjecture and the log–Brunn–Minkowski inequality (2016, background): “For o-symmetric convex bodies K and L, Böröczky, Lutwak, Yang, and Zhang [5] also established the following log-Minkowski inequality:∫ S1 log hL hK dVK ≥ |K| 2 log |L| |K| .”
New Orlicz affine isoperimetric inequalities (2014, background): “Important contributions include the study of Logarithmic Minkowski and even Orlicz Minkowski problems [7, 15]; the logBrunn-Minkowski-inequality [5]; stronger versions of the Orlicz-Petty projection inequality [6]; Orlicz Busemann-Petty centroid inequality [10, 20, 53] among others.”
On the stability of Brunn–Minkowski type inequalities (2016, methodology): “It is not difficult to see that the condition of symmetry is necessary (see [6] or Remark 1.”
The logarithmic Minkowski problem for polytopes (2014, background): “Uniqueness for the logarithmic Minkowski problem was completely settled for even measures in R(2) in [7].”
THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES (2013, background): “for o-symmetric convex bodies K and L, proved by Böröczky, Lutwak, Yang, and Zhang [2] when n = 2 and conjectured by them to hold for all n ≥ 2.”
The discrete logarithmic Minkowski problem (2014, neutral): “alities established by Lutwak [43]. One reason that the Lp Minkowski problem becomes challenging when p < 1 is because little is known about the mixed volume inequalities when p < 1 (see, e.g., [7]). The L 0 is called the logarithmic case, is clearly the most important case with geometric sign”
The dimensional Brunn–Minkowski inequality in Gauss space (2020, background): “The log-Brunn–Minkowski conjecture of [BLYZ12], asserts that for any such sets and λ ∈ (0, 1), ∣∣KλL1−λ∣∣ > |K|λ|L|1−λ.”
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”