Results 61 to 70 of about 813 (131)
Sharp affine weighted L 2 Sobolev inequalities on the upper half space
Advanced Nonlinear StudiesWe establish some sharp affine weighted L 2 Sobolev inequalities on the upper half space, which involves a divergent operator with degeneracy on the boundary.
Dou Jingbo, Hu Yunyun, Yue Caihui
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Gaussian Brunn-Minkowski inequalities
, 2020 . A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality is proved, together with precise equality conditions, and shown to be best possible from several points of view.
Artem Zvavitch, Richard J Gardner
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Sharp quantitative stability of the Brunn-Minkowski inequality
, 2023 The Brunn-Minkowski inequality states that for bounded measurable sets $A$ and $B$ in $\mathbb{R}^n$, we have $|A+B|^{1/n} \geq |A|^{1/n}+|B|^{1/n}$. Also, equality holds if and only if $A$ and $B$ are convex and homothetic sets in $\mathbb{R}^d$.
van Hintum, Peter +2 more
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Quantitative stability for the Brunn–Minkowski inequality
, 2019 © 2016 We prove a quantitative stability result for the Brunn–Minkowski inequality: if |A|=|B|=1, t∈[τ,1−τ] with τ>0, and |tA+(1−t)B|1/n≤1+δ for some small δ, then, up to a translation, both A and B are quantitatively close (in terms of δ) to a convex ...
Jerison, David +2 more
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Dual
Journal of Inequalities and Applications, 2006 We establish some inequalities for the dual -centroid bodies which are the dual forms of the results by Lutwak, Yang, and Zhang. Further, we establish a Brunn-Minkowski-type inequality for the polar of dual -centroid bodies.
Bin Xiong, Wuyang Yu, Lin Si
doaj
The strong Brunn--Minkowski inequality and its equivalence with the CD condition
, 2022 In the setting of essentially non-branching metric measure spaces, we prove the equivalence between the curvature dimension condition CD(K,N), in the sense of Lott--Sturm--Villani, and a newly introduced notion that we call strong Brunn--Minkowski ...
Rossi, Tommaso +2 more
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The Brunn–Minkowski–Firey inequality for nonconvex sets
, 2012 The definition of Minkowski–Firey Lp-combinations is extended from convex bodies to arbitrary subsets of Euclidean space. The Brunn–Minkowski–Firey inequality (along with its equality conditions), previously established only for convex bodies, is shown ...
Lutwak, Erwin +5 more
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Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems. [PDF]
Entropy (Basel), 2022 Sason I.
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A discrete version and stability of Brunn Minkowski inequality
, 2009 International audienceIn the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for length spaces.
Bonnefont, Michel
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On the stability of Brunn–Minkowski type inequalities
, 2017 We establish the stability near a Euclidean ball of two conjectured inequalities: the dimensional Brunn–Minkowski inequality for radially symmetric log-concave measures in Rn, and of the log-Brunn–Minkowski ...
Livshyts, Galyna V. +5 more
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