Entropy and asymptotic geometry of non-symmetric convex bodies
From MaRDI portal
Publication:1578074
DOI10.1006/aima.1999.1903zbMath0974.52004OpenAlexW2072611242MaRDI QIDQ1578074
Publication date: 27 August 2000
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/2bed9325a568c069bffe45847408572066cbf778
Local theory of Banach spaces (46B07) Inequalities and extremum problems involving convexity in convex geometry (52A40) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items
Improved bounds for Hadwiger's covering problem via thin-shell estimates, The Slicing Problem by Bourgain, When random proportional subspaces are also random quotients, Diameters of sections and coverings of convex bodies, Covering convex bodies and the closest vector problem, Product set estimates for non-commutative groups, Isotropic constants and Mahler volumes, Rogers-Shephard inequality for log-concave functions, Functional covering numbers, Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures, ARRANGEMENTS OF HOMOTHETS OF A CONVEX BODY, On the volume ratio of projections of convex bodies, On a generalization of the Hermite-Hadamard inequality and applications in convex geometry, More on the duality conjecture for entropy numbers., The Alon–Milman Theorem for Non-symmetric Bodies, Entropy numbers of finite-dimensional embeddings, A reverse Rogers-Shephard inequality for log-concave functions, Estimates for the affine and dual affine quermassintegrals of convex bodies, Small ball probability estimates for log-concave measures, The isotropic position and the reverse Santaló inequality, On approximation by projections of polytopes with few facets, Geometry of sets of quantum maps: A generic positive map acting on a high-dimensional system is not completely positive, A randomized sieving algorithm for approximate integer programming, A remark on the slicing problem, Extremal general affine surface areas, Covering a set with homothets of a convex body, An isomorphic version of the slicing problem, Entanglement Thresholds for Random Induced States, Small ball probability estimates, \(\psi_2\)-behavior and the hyperplane conjecture, An example of a convex body without symmetric projections, On the log-Minkowski inequality for simplices and parallelepipeds, Estimating the average of functions with convexity properties by means of a new center, Lattice Point Inequalities for Centered Convex Bodies, On some covering problems in geometry, k-Extendibility of high-dimensional bipartite quantum states, Extremal problems and isotropic positions of convex bodies, Positions of convex bodies associated to extremal problems and isotropic measures, Deterministic Construction of an Approximate M-Ellipsoid and its Application to Derandomizing Lattice Algorithms, Tropical varieties for exponential sums, Proportional concentration phenomena on the sphere, Variations of Minkowski's theorem on successive minima, Functional John ellipsoids
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The difference body of a convex body
- Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
- The dimension of almost spherical sections of convex bodies
- Global versus local asymptotic theories of finite-dimensional normed spaces
- New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
- Distances between non-symmetric convex bodies and the \(MM^*\)-estimate
- An Inequality for Sections and Projections of a Convex Set
- Convex Bodies Associated with a Given Convex Body
- Almost Euclidean Quotient Spaces of Subspaces of a Finite-Dimensional Normed Space
- The covering numbers and “low 𝑀*-estimate" for quasi-convex bodies
- Covering convex bodies by translates of convex bodies
