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

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Publications

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
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
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
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
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
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
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
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
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
DOI: 10.1016/j.aim.2018.06.014

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
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
DOI: 10.1007/978-3-319-45282-1_7