Results 91 to 100 of about 4,011 (135)

The Dual Hamilton–Jacobi Equation and the Poincaré Inequality

Mathematics
Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarithmic ...
Rigao He, Wei Wang, Jianglin Fang, Yuanlin Li   +3 more
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Brunn–Minkowski and Zhang inequalities for convolution bodies

Advances in Mathematics, 2013
22 pages.
Alonso Gutiérrez, David, Jiménez Gómez, Carlos Hugo, Villa Caro, Rafael   +2 more
openaire   +6 more sources

Sharp affine weighted L 2 Sobolev inequalities on the upper half space

Advanced Nonlinear Studies
We 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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A (one-dimensional) free Brunn–Minkowski inequality

Comptes Rendus. Mathématique, 2005
We present a one-dimensional version of the functional form of the geometric Brunn–Minkowski inequality in free (non-commutative) probability theory. The proof relies on matrix approximation as used recently by Biane and Hiai et al. to establish free analogues of the logarithmic Sobolev and transportation cost inequalities for strictly convex ...
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Dual affine isoperimetric inequalities

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 Reverse-log-Brunn-Minkowski inequality

, 2023
Firstly, we propose our conjectured Reverse-log-Brunn-Minkowski inequality (RLBM). Secondly, we show that the (RLBM) conjecture is equivalent to the log-Brunn-Minkowski (LBM) conjecture proposed by Böröczky-Lutwak-Yang-Zhang. We name this as ``reverse-to-forward" principle.
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Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems. [PDF]

Entropy (Basel), 2022
Sason I.
europepmc   +1 more source

The Brunn–Minkowski–Firey inequality for nonconvex sets

Advances in Applied Mathematics, 2012
In this short note, the authors first extend the definition of Minkowski-Firey \(L_p\)-combinations from convex bodies to arbitrary subsets of Euclidean space, and then prove the Brunn-Minkowski-Firey inequality for compact (not necessarily convex) sets of \(\mathbb{R}^n\).
Lutwak, Erwin, Yang, Deane, Zhang, Gaoyong   +2 more
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Brunn-Minkowski Inequality for θ-Convolution Bodies via Ball's Bodies. [PDF]

J Geom Anal
Alonso-Gutiérrez D, Goñi JM.
europepmc   +1 more source

Error Resilient Space Partitioning. [PDF]

Discrete Comput Geom
Dunkelman O, Geyzel Z, Keller C, Keller N, Ronen E, Shamir A, Tessler RJ.   +6 more
europepmc   +1 more source