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

Project Information

CONC-VIA-RIEMANN

Grant agreement ID: 637851

DOI 10.3030/637851

Project closed

EC signature date 4 June 2015

Start date 1 October 2015

End date 30 September 2021

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 194 190,00

EU contribution € 1 194 190,00

Coordinated by

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Israel

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (20)

Sharp Poincaré inequalities under Measure Contraction Property

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

Local $L^p$-Brunn-Minkowski inequalities for $p<1$

Author(s): Alexander V. Kolesnikov, Emanuel Milman
Published in: Memoirs of the American Mathematical Society, 2022, ISSN 0065-9266
Publisher: American Mathematical Society

Measure rigidity of synthetic lower Ricci curvature bound on Riemannian manifolds

Author(s): Bang-Xian Han
Published in: Advances in Mathematics, Issue 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, Issue 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, Issue 226/1, 2021, Page(s) 1-137, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-021-01040-6

The Gaussian Double-Bubble and Multi-Bubble Conjectures

Author(s): Emanuel Milman, Joe Neeman
Published in: Annals of Mathematics, Issue 195, 2022, Page(s) 1-118, ISSN 0003-486X
Publisher: Princeton University Press

Rigidity of some functional inequalities on RCD spaces

Author(s): Bang-Xian Han
Published in: Journal de Mathématiques Pures et Appliquées, Issue 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, Issue 67/1, 2021, Page(s) 81-94, ISSN 0018-9448
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tit.2020.3032371

Reverse Hlder inequalities for log-Lipschitz functions

Author(s): Emanuel Milman
Published in: Pure and Applied Functional Analysis, 2022, ISSN 2189-3756
Publisher: Yokohama Publishers

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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 334, 2018, Page(s) 389-416, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2018.06.014

Some applications of the heat flow to Laplace eigenfunctions

Author(s): Bogdan Georgiev, Mayukh Mukherjee
Published in: Communications in Partial Differential Equations, 2022, ISSN 0360-5302
Publisher: Marcel Dekker Inc.

Other (4)

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

Thesis and dissertations (1)

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

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

Book chapters (3)

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, Issue 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, Issue 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, Issue 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