Results 21 to 30 of about 671 (71)
Open Mathematics, 2018 In this paper, by the Orlicz-Minkowski combinations of convex bodies, we define the general Orlicz difference bodies and study their properties. Furthermore, we obtain the extreme values of the general Orlicz difference bodies and their polars.
Shi Wei, Wang Weidong, Ma Tongyi
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On the polyhedral cones of convex and concave vectors [PDF]
, 2013 Convex or concave sequences of n positive terms, viewed as vectors in n-space, constitute convex cones with 2n − 2 and n extreme rays, respectively.
Foldes, Stephan, Major, Laszlo
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On the perimeters of simple polygons contained in a disk
, 2010 A simple $n$-gon is a polygon with $n$ edges with each vertex belonging to exactly two edges and every other point belonging to at most one edge. Brass asked the following question: For $n \geq 5$ odd, what is the maximum perimeter of a simple $n$-gon ...
C. Audet, P. Brass, Zsolt Lángi
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A Blichfeldt-type inequality for centrally symmetric convex bodies
, 2012 In this note, we derive an asymptotically sharp upper bound on the number of lattice points in terms of the volume of centrally symmetric convex bodies.
Henze, Matthias
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Approximate Gaussian isoperimetry for k sets [PDF]
, 2011 Given $2\le k\le n$, the minimal $(n-1)$-dimensional Gaussian measure of the union of the boundaries of $k$ disjoint sets of equal Gaussian measure in $\R^n$ whose union is $\R^n$ is of order $\sqrt{\log k}$.
Schechtman, Gideon
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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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A remark on perimeter-diameter and perimeter-circumradius inequalities under lattice constraints [PDF]
, 2013 In this note, we study several inequalities involving geometric functionals for lattice point-free planar convex sets.
Henze, Matthias +1 more
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Optimal Concentration of Information Content For Log-Concave Densities
, 2015 An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean.
A. Prékopa +18 more
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The Fenchel-type inequality in the 3-dimensional Lorentz space and a Crofton formula
, 2016 We generalize the Fenchel theorem to strong spacelike (which means that the tangent vector and the curvature vector span a spacelike 2-plane at each point) closed curves with index 1 in the 3-dimensional Lorentz space, showing that the total curvatures ...
Ma, Xiang, Wang, Donghao, Ye, Nan
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Minimality of planes in normed spaces
, 2012 We prove that a region in a two-dimensional affine subspace of a normed space $V$ has the least 2-dimensional Hausdorff measure among all compact surfaces with the same boundary.
A.C. Thompson +12 more
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