The Santaló point of a function, and a functional form of the Santaló inequality
From MaRDI portal
Publication:5479474
DOI10.1112/S0025579300015497zbMath1121.52021OpenAlexW2123539931MaRDI QIDQ5479474
Bo'az Klartag, Vitali D. Milman, Shiri Artstein-Avidan
Publication date: 10 July 2006
Published in: Mathematika (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/s0025579300015497
Geometry and structure of normed linear spaces (46B20) Inequalities and extremum problems involving convexity in convex geometry (52A40) Inequalities for sums, series and integrals (26D15)
Related Items
Stability for Borell-Brascamp-Lieb Inequalities, LYZ ellipsoid and Petty projection body for log-concave functions, Convex bodies and norms associated to convex measures, Some functional forms of Blaschke-Santaló inequality, Rogers-Shephard inequality for log-concave functions, CONCAVITY PROPERTIES OF EXTENSIONS OF THE PARALLEL VOLUME, John's ellipsoid and the integral ratio of a log-concave function, The equality cases in Steiner's projection inequality, Functional inequalities related to Mahler's conjecture, The Löwner function of a log-concave function, Functional covering numbers, SYMMETRIZED TALAGRAND INEQUALITIES ON EUCLIDEAN SPACES, Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties, On weighted covering numbers and the Levi-Hadwiger conjecture, On the framework of \(L_p\) summations for functions, New mixed star bodies and related volume inequalities, Floating functions, A zoo of dualities, Some remarks on petty projection of log-concave functions, To logconcavity and beyond, q-Moment Measures and Applications: A New Approach via Optimal Transport, Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality, Projection body and isoperimetric inequalities for \(s\)-concave functions, The Grassmannian \(L_p\)-sine Blaschke-Santaló inequality, Pointillisme à la Signac and construction of a quantum fiber bundle over convex bodies, On a \(j\)-Santaló conjecture, Functional geominimal surface area and its related affine isoperimetric inequality, Several Results Regarding the (B)-Conjecture, The geometry of \(p\)-convex intersection bodies, Stability of the functional forms of the Blaschke-Santaló inequality, Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities, The first variation of the total mass of log-concave functions and related inequalities, Equivariant endomorphisms of convex functions, Stability of the Blaschke-Santaló and the affine isoperimetric inequality, A characterization of duality through section/projection correspondence in the finite dimensional setting, A Santaló-type inequality for the 𝒥 transform, Divergence for \(s\)-concave and log concave functions, A sharp Blaschke-Santaló inequality for \(\alpha \)-concave functions, The concept of duality for measure projections of convex bodies, A new approach to Steiner symmetrization of coercive convex functions, Minimal volume product near Hanner polytopes, Some functional inverse Santaló inequalities, The mixed Lp affine surface areas for functions, A stochastic Prékopa–Leindler inequality for log-concave functions, Invariant Valuations on Super-Coercive Convex Functions, Increasing functions and inverse Santaló inequality for unconditional functions, Further inequalities for the (generalized) Wills functional, Functional Löwner ellipsoids, Mass transport and variants of the logarithmic Sobolev inequality, A sharp symmetrized form of Talagrand's transport-entropy inequality for the Gaussian measure, A new duality transform, Stability of the reverse Blaschke-Santaló inequality for zonoids and applications, Halfspace depth and floating body, Asymmetric Blaschke-Santaló functional inequalities, Mixedf-divergence and inequalities for log-concave functions, Hidden structures in the class of convex functions and a new duality transform, A note on Santaló inequality for the polarity transform and its reverse, Stability of the reverse Blaschke-Santaló inequality for unconditional convex bodies, Characterization of self-polar convex functions, Euclidean forward-reverse Brascamp-Lieb inequalities: finiteness, structure, and extremals, The case of equality for an inverse Santaló functional inequality, Estimates of norms of log-concave random matrices with dependent entries, Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory, The symmetric property \((\tau )\) for the Gaussian measure, A direct proof of the functional Santaló inequality, Quantitative Borell-Brascamp-Lieb inequalities for compactly supported power concave functions (and some applications), The isomorphic Busemann-Petty problem for \(s\)-concave measures, Complex integrals and Kuperberg's proof of the Bourgain-Milman theorem, An extension of Berwald's inequality and its relation to Zhang's inequality, Orlicz Addition for Measures and an Optimization Problem for the -divergence, Best approximation of functions by log-polynomials, Rogers-Shephard and local Loomis-Whitney type inequalities, Blaschke-Santaló inequality for many functions and geodesic barycenters of measures, A Riesz representation theorem for functionals on log-concave functions, A characterization of the support map, The Busemann-Petty problem on entropy of log-concave functions, Surface area measures of log-concave functions, Geometry of log-concave functions and measures, Moment measures, Pinsker inequalities and related Monge-Ampere equations for log-concave functions, Geometry of log-concave functions: the \(L_p\) Asplund sum and the \(L_p\) Minkowski problem, The functional version of the Ball inequality, Affine invariant maps for log-concave functions, Functional John ellipsoids
Cites Work