John and Loewner ellipsoids

DOI10.1007/s00454-011-9354-8zbMath1241.52002OpenAlexW2028140316MaRDI QIDQ650104

Peter M. Gruber

Publication date: 25 November 2011

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-011-9354-8

zbMATH Keywords

convex bodyJohn ellipsoidLoewner ellipsoideutaxymaximum volumeperfection

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (19)

ON SOME RELATIONS BETWEEN THE CONE OF POSITIVE SEMIDEFINITE MATRICES AND THE MOMENT CONE ⋮ The logarithmic John ellipsoid ⋮ Orlicz-Legendre ellipsoids ⋮ Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds ⋮ Solving continuous set covering problems by means of semi-infinite optimization. With an application in product portfolio optimization ⋮ The minimal Orlicz surface area ⋮ Measuring centrality and dispersion in directional datasets: the ellipsoidal cone covering approach ⋮ An \(\text{SL}(n)\)-invariant mixed integral \(L_p\) affine surface area ⋮ Orlicz-John ellipsoids ⋮ Minimal area ellipses in the hyperbolic plane ⋮ Normal bundles of convex bodies ⋮ \((p, q)\)-John ellipsoids ⋮ Conic version of Loewner-John ellipsoid theorem ⋮ Quantitative combinatorial geometry for concave functions ⋮ Lattice packing and covering of convex bodies ⋮ Application of an idea of Voronoĭ to lattice zeta functions ⋮ On mixed \(L_{p}\) John ellipsoids ⋮ A sharp dual \(L_p\) John ellipsoid problem for \(p\le -n-1\) ⋮ The minimal Orlicz mean width of convex bodies

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• Minima of Epstein's zeta function and heights of flat tori
• Voronoĭ type criteria for lattice coverings with balls
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