Results 11 to 20 of about 187 (48)
Symmetrization in Geometry [PDF]
, 2016 The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets.
Bianchi, G., Gardner, R. J., Gronchi, P.
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A sausage body is a unique solution for a reverse isoperimetric problem
, 2019 We consider the class of $\lambda$-concave bodies in $\mathbb R^{n+1}$; that is, convex bodies with the property that each of their boundary points supports a tangent ball of radius $1/\lambda$ that lies locally (around the boundary point) inside the ...
Chernov, Roman +2 more
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Forum of Mathematics, SigmaA spectral convex set is a collection of symmetric matrices whose range of eigenvalues forms a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal–Sottile–Sturmfels (2011). We study this class of convex bodies,
Raman Sanyal, James Saunderson
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Lorentzian polynomials on cones
Forum of Mathematics, SigmaInspired by the theory of hyperbolic polynomials and Hodge theory, we develop the theory of Lorentzian polynomials on cones. This notion captures the Hodge-Riemann relations of degree zero and one.
Petter Brändén, Jonathan Leake
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Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields [PDF]
, 2012 Consider a $d\times d$ matrix $M$ whose rows are independent centered non-degenerate Gaussian vectors $\xi_1,...,\xi_d$ with covariance matrices $\Sigma_1,...,\Sigma_d$. Denote by $\mathcal{E}_i$ the location-dispersion ellipsoid of $\xi_i:\mathcal{E}_i={
Kabluchko, Zakhar, Zaporozhets, Dmitry
core
Equality cases of the Alexandrov–Fenchel inequality are not in the polynomial hierarchy
Forum of Mathematics, PiDescribing the equality conditions of the Alexandrov–Fenchel inequality [Ale37] has been a major open problem for decades. We prove that in the case of convex polytopes, this description is not in the polynomial hierarchy unless the polynomial hierarchy ...
Swee Hong Chan, Igor Pak
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Geometric properties of the family of p-parallel bodies
Analysis and Geometry in Metric SpacesWe study geometric properties of the family of p-parallel bodies of a convex body K with respect to a gauge body E. In particular, we investigate various regularity properties of their boundaries by means of their 0-extreme vectors, aiming for extensions
Hernández Cifre María A. +2 more
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Characterizing the dual mixed volume via additive functionals [PDF]
, 2013 Integral representations are obtained of positive additive functionals on finite products of the space of continuous functions (or of bounded Borel functions) on a compact Hausdorff space.
Dulio, Paolo +2 more
core
A characterization of Blaschke addition
, 2014 A characterization of Blaschke addition as a map between origin-symmetric convex bodies is established. This results from a new characterization of Minkowski addition as a map between origin-symmetric zonoids, combined with the use of L\'{e}vy-Prokhorov ...
Gardner, Richard J. +2 more
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Poisson polyhedra in high dimensions
, 2015 The zero cell of a parametric class of random hyperplane tessellations depending on a distance exponent and an intensity parameter is investigated, as the space dimension tends to infinity.
Hoerrmann, Julia +3 more
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