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High-Dimensional Convexity, Isoperimetry and Concentration via a Riemannian Vantage Point

Publications

Sharp Poincaré inequalities under Measure Contraction Property

Author(s): Bang-Xian Han, Emanuel Milman
Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, XXII, 2021, Page(s) 1401-1428, ISSN 0391-173X
Publisher: Stampacchia Guido
DOI: 10.2422/2036-2145.201906_012

Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds

Author(s): Bang-Xian Han
Published in: Advances in Mathematics, 373, 2020, Page(s) 107327, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2020.107327

The Quasi Curvature‐Dimension Condition with Applications to Sub‐Riemannian Manifolds

Author(s): Emanuel Milman
Published in: Communications on Pure and Applied Mathematics, 74/12, 2021, Page(s) 2628-2674, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.21969

The globalization theorem for the Curvature-Dimension condition

Author(s): Fabio Cavalletti, Emanuel Milman
Published in: Inventiones mathematicae, 226/1, 2021, Page(s) 1-137, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-021-01040-6

Rigidity of some functional inequalities on RCD spaces

Author(s): Bang-Xian Han
Published in: Journal de Mathématiques Pures et Appliquées, 145, 2021, Page(s) 163-203, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.1016/j.matpur.2020.07.004

Sharp Moment-Entropy Inequalities and Capacity Bounds for Symmetric Log-Concave Distributions

Author(s): Mokshay Madiman, Piotr Nayar, Tomasz Tkocz
Published in: IEEE Transactions on Information Theory, 67/1, 2021, Page(s) 81-94, ISSN 0018-9448
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tit.2020.3032371

Bounds on Moments of Weighted Sums of Finite Riesz Products

Author(s): Aline Bonami, Rafał Latała, Piotr Nayar, Tomasz Tkocz
Published in: Journal of Fourier Analysis and Applications, 26/6, 2020, ISSN 1069-5869
Publisher: Birkhaeuser
DOI: 10.1007/s00041-020-09800-3

Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds

Author(s): Alexander V. Kolesnikov, Emanuel Milman
Published in: American Journal of Mathematics, 140/5, 2018, Page(s) 1147-1185, ISSN 1080-6377
Publisher: John Hopkins University Press
DOI: 10.1353/ajm.2018.0027

The KLS isoperimetric conjecture for generalized Orlicz balls

Author(s): Alexander V. Kolesnikov, Emanuel Milman
Published in: The Annals of Probability, 46/6, 2018, Page(s) 3578-3615, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/18-AOP1257

Generalized dual Sudakov minoration via dimension-reduction—a program

Author(s): Shahar Mendelson, Emanuel Milman, Grigoris Paouris
Published in: Studia Mathematica, 244/2, 2019, Page(s) 159-202, ISSN 0039-3223
Publisher: Polska Akademia Nauk
DOI: 10.4064/sm170519-1-9

Brascamp–Lieb-Type Inequalities on Weighted Riemannian Manifolds with Boundary

Author(s): Alexander V. Kolesnikov, Emanuel Milman
Published in: The Journal of Geometric Analysis, 27/2, 2017, Page(s) 1680-1702, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-016-9736-5

Riemannian metrics on convex sets with applications to Poincaré and log-Sobolev inequalities

Author(s): Alexander V. Kolesnikov, Emanuel Milman
Published in: Calculus of Variations and Partial Differential Equations, 55/4, 2016, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-016-1018-3

Spectral estimates, contractions and hypercontractivity

Author(s): Emanuel Milman
Published in: Journal of Spectral Theory, 8/2, 2018, Page(s) 669-714, ISSN 1664-039X
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jst/210

Sharp p-Poincaré inequalities under measure contraction property

Author(s): Bang-Xian Han
Published in: manuscripta mathematica, 2019, ISSN 0025-2611
Publisher: Springer Verlag
DOI: 10.1007/s00229-019-01138-5

Polyhedral Billiards, Eigenfunction Concentration and Almost Periodic Control

Author(s): Mihajlo Cekić, Bogdan Georgiev, Mayukh Mukherjee
Published in: Communications in Mathematical Physics, 2020, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-020-03741-0

Sharp comparison of moments and the log-concave moment problem

Author(s): Alexandros Eskenazis, Piotr Nayar, Tomasz Tkocz
Published in: Advances in Mathematics, 334, 2018, Page(s) 389-416, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2018.06.014

On the asymptotic behaviour of the fractional Sobolev seminorms in metric measure spaces: Bourgain-Brezis-Mironescu's theorem revisited

Author(s): Bang-Xian Han, Andrea Pinamonti
Published in: Submitted to peer reviewed journal, 2023
Publisher: N/A

A sharp centro-affine isospectral inequality of Szegö–Weinberger type and the L^p-Minkowski problem

Author(s): Emanuel Milman
Published in: Submitted to peer reviewed journal, 2023
Publisher: International Press

Centro-affine differential geometry and the log-Minkowski problem

Author(s): Emanuel Milman
Published in: Submitted to peer reviewed journal, 2023
Publisher: European Mathematical Society

Sharp Isoperimetric Inequalities for Affine Quermassintegrals

Author(s): Emanuel Milman, Amir Yehudayoff
Published in: Submitted to peer reviewed journal, 2023
Publisher: American Mathematical Society

Functional Inequalities on Weighted Riemannian Manifolds Subject to Curvature-Dimension Conditions

Author(s): Eran Calderon
Published in: 2019
Publisher: Technion - Israel Institute of Technology

Sharp Poincar\'e-type inequality for the Gaussian measure on the boundary of convex sets

Author(s): Alexander V. Kolesnikov, Emanuel Milman
Published in: Lecture Notes in Mathematics, 2169, 2017, Page(s) 221-234
Publisher: Springer International Publishing
DOI: 10.1007/978-3-319-45282-1_15

An inequality for moments of log-concave functions on Gaussian random vectors

Author(s): Nikos Dafnis, Grigoris Paouris
Published in: Lecture Notes in Mathematics, 2169, 2017, Page(s) 107-122
Publisher: Springer International Publishing
DOI: 10.1007/978-3-319-45282-1_7

Two Remarks on Generalized Entropy Power Inequalities

Author(s): Mokshay Madiman, Piotr Nayar, Tomasz Tkocz
Published in: Geometric Aspects of Functional Analysis - Israel Seminar (GAFA) 2017-2019 Volume II, 2266, 2020, Page(s) 169-185, ISBN 978-3-030-46761-6
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-46762-3_7