Preprints and Manuscripts:

  • Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs, submitted. [arXiv link]
  • with Mohammad N. Ivaki, L^p-Minkowski problem under curvature pinching, to appear in Int. Math. Res. Not. (IMRN). [arXiv link]
  • with Joe Neeman, Plateau bubbles and the Quintuple Bubble Theorem on S^n, submitted. [arXiv link]
  • with Mohammad N. Ivaki, Uniqueness of solutions to a class of isotropic curvature problems, to appear in Adv. Math. 435 (109350). [arXiv link]
  • with Joe Neeman, The structure of isoperimetric bubbles in R^n and S^n, to appear in Acta Math. [arXiv link]
    See also Quanta article and AMR video.
  • Centro-affine differential geometry and the log-Minkowski problem, to appear in J. Eur. Math. Soc. [arXiv link]
  • A sharp centro-affine isospectral inequality of Szegö–Weinberger type and the L^p-Minkowski problem, to appear in J. Differ. Geom. [arXiv link]

Publications (according to topic):

Isoperimetric And Functional Inequalities

  • with Amir Yehudayoff, Sharp Isoperimetric Inequalities for Affine Quermassintegrals, J. Amer. Math. Soc. 36 (4), 1061-1101, 2023. [arXiv link]
  • Reverse Hölder inequalities for log-Lipschitz functions, Pure Appl. Funct. Anal. 8 (1), 297-310, 2023, special issue dedicated to Louis Nirenberg. [arXiv link]
  • with Joe Neeman, The Gaussian Double-Bubble and Multi-Bubble Conjectures, Annals of Math. 195, 89-206, 2022. [arXiv link]
  • with Fabio Cavalletti, The globalization theorem for the Curvature-Dimension condition, Invent. Math. 226, 1–137, 2021 (Recepient of Frontiers of Science Award 2024). [arXiv link]
  • The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds, Comm. Pure Appl. Math. (CPAM) 74 (12) 2628-2674, 2021. [arXiv link]
  • with Bang-Xian Han, Sharp Poincaré  Inequalities under Measure Contraction Property, Ann. Sc. Norm. Super. Pisa Cl. Sci.(5) XXII (3), 1401-1428, 2021. [arXiv link]
  • with Alexander Kolesnikov, Local L^p-Brunn-Minkowski inequalities for p<1, Mem. Amer. Math. Soc. 277 (1360), v+78 pp, 2022. [arXiv link]
  • with Alexander Kolesnikov, The KLS isoperimetric conjecture for generalized Orlicz balls, Ann. Probab. 46 (6), 3578–3615 , 2018. [arXiv link]
  • with Alexander KolesnikovPoincaré and Brunn–Minkowski inequalities on the boundary of weighted Riemannian manifolds, Amer. J. Math.  140 (5), 1147-1185, 2018. [arXiv link]
  • Spectral Estimates, Contractions and Hypercontractivity, J. Spectr. Theory 8 (2), 669–714, 2018. [arXiv link]
  • Harmonic Measures on the Sphere via Curvature-Dimension, Annales de la Faculté des Sciences de Toulouse 26 (2), 437-449, 2017. [arXiv link]
  • with Alexander Kolesnikov, Sharp Poincare-type inequality for the Gaussian measure on the boundary of convex sets, Lecture Notes in Math. 2169, GAFA Seminar Notes 2014–2016, 221-234, 2017. [arXiv link]
  • Beyond traditional Curvature-Dimension I: new model spaces for isoperimetric and concentration inequalities in negative dimension, Trans. Amer. Math. Soc. 369, 3605-3637, 2017. [arXiv link]
  • with Alexander Kolesnikov, Brascamp–Lieb type inequalities on weighted Riemannian manifolds with boundary, J. Geom. Anal. 27 (2), 1680-1702, 2017. [arXiv link]
  • with Alexander Kolesnikov, Riemannian metrics on convex sets with applications to Poincaré and log-Sobolev inequalities, Calc. Var. & PDE 55: 77, 2016, [arXiv link]
  • with Alexander Kolesnikov, Riemannian metrics and Sobolev-type inequalities, Doklady Akademii Nauk 470 (2), 1-4, 2016 (in Russian).
  • Sharp Isoperimetric Inequalities and Model Spaces for Curvature-Dimension-Diameter Condition, J. Eur. Math. Soc. 17 (5), 1041–1078, 2015. [arXiv link]
  • with Alexander Kolesnikov, Isoperimetric Inequalities on Weighted Manifolds with Boundary, Doklady Akademii Nauk 464 (2), 136–140, 2015 (in Russian).
  • with Alexander Kolesnikov, Remarks on KLS conjecture and Hardy-type inequalities, Lecture Notes in Math. 2116, GAFA Seminar Notes 2011–2013, 273-292, 2014. [arXiv link]
  • with Liran Rotem, Complemented Brunn-Minkowski Inequalities and Isoperimetry for Homogeneous and Non-Homogeneous Measures, Adv. Math. 262, 867-908, 2014. [arXiv link]
  • with Franck Barthe, Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems, Comm. Math. Physics 323, 575–625, 2013. [arXiv link]
  • A Proof of Bobkov’s Spectral Bound For Convex Domains via Gaussian Fitting and Free Energy Estimation, Centre de Recherches Mathématiques, CRM Proceedings and Lecture Notes, Vol. 56, 181-196, 2013. [arXiv link]
  • Model Spaces for Sharp Isoperimetric Inequalities, C. R. Math. Acad. Sci. Paris 350, 897-902, 2012. [pdf]
  • Properties of Isoperimetric, Functional and Transport-Entropy Inequalities Via Concentration, Probab. Theory Relat. Fields 152, 475–507, 2012. [arXiv link]
  • with Young-Heon Kim, A Generalization of Caffarelli’s Contraction Theorem via (reverse) Heat Flow, Math. Annal. 354 (3), 827-862, 2012. [arXiv link]
  • Isoperimetric Bounds on Convex Manifolds, “Concentration, Functional Inequalities and Isoperimetry”, Contemporary Mathematics 545, Amer. Math. Soc., 195-208, 2011. [arXiv link]
  • A converse to the Maz’ya inequality for capacities under curvature lower bound, Springer’s International Mathematical Series Vol. 11, Around the Research of Vladimir Maz’ya I. Function Spaces, 321-348. [arXiv link]
  • Isoperimetric and Concentration Inequalities – Equivalence under Curvature Lower Bound, Duke Math. J. 154 (2), 207-239, 2010. [arXiv link]
  • Concentration and isoperimetry are equivalent assuming curvature lower bound, C. R. Math. Acad. Sci. Paris. 347, 73-76, 2009. [pdf]
  • On the role of convexity in functional and isoperimetric inequalities, Proc. London Math. Soc. 99 (3), 32-66, 2009. [arXiv link]
  • On the role of convexity in isoperimetry, spectral gap and concentration,  Invent. Math. 177 (1), 1-43, 2009. [arXiv link]
  • Uniform tail-decay of Lipschitz functions implies Cheeger’s isoperimetric inequality under convexity assumptions, C. R. Math. Acad. Sci. Paris 346, 989-994, 2008. [pdf]
  • with Sasha Sodin, An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies, J. Func. Anal. 254 (5), 1235-1268, 2008. [arXiv link]

Distribution of Volume in Convex Bodies

  • with Yuval Yifrach, Regular Random Sections of Convex Bodies and the Random Quotient-of-Subspace Theorem, J. Func. Anal. 281 (7) 109133, 2021. [arXiv link]
  • with Vitali Milman and Liran Rotem, Reciprocals and Flowers in Convexity, Lecture Notes in Math. 2266, GAFA Seminar Notes 2017–2019, 199-227, 2020. [arXiv link]
  • with Shahar Mendelson and Grigoris Paouris, Generalized Dual Sudakov Minoration via Dimension Reduction – A Program, Studia Math. 244, 159-202, 2019. [arXiv link]
  • On the mean-width of isotropic convex bodies and their associated Lp-centroid bodies, Int. Math. Res. Not. 11, 3408–3423, 2015. [arXiv link]
  • with Apostolos Giannopoulos, M-estimates for isotropic convex bodies and their Lq-centroid bodies, , Lecture Notes in Math. 2116, GAFA Seminar Notes 2011–2013, 159-182, 2014. [arXiv link]
  • with Bo’az KlartagInner Regularization of Log-Concave Measures and Small-Ball Estimates, Lecture Notes in Math. 2050, GAFA Seminar Notes 2006–2010, 267-278, 2012. [arXiv link]
  • with Bo’az Klartag, Centroid Bodies and the Logarithmic Laplace Transform – A Unified Approach, J. Func. Anal. 262 (1), 10-34, 2012. [arXiv link]
  • with Olivier GuedonInterpolating Thin-Shell and Sharp Large-Deviation Estimates For Isotropic Log-Concave Measures, Geom. Funct. Anal. 21 (5), 1043-1068, 2011. [arXiv link]
  • On Gaussian marginals of uniformly convex bodies, J. Theor. Prob. 22 (1), 256-278, 2009. [arXiv link]
  • with Bo’az Klartag, On volume distribution in 2-convex bodies, Israel J. Math. 164, 221-249, 2008. [arXiv link]
  • A remark on two duality relations, Integral Equations and Operator Theory 57 (2), 217-228, 2007. [arXiv link]
  • Dual mixed volumes and the Slicing Problem, Adv. Math. 207 (2), 566-598, 2006. [arXiv link]

Low-Dimensional Sections of Star Bodies

  • Generalized Intersection Bodies are not equivalent, Adv. Math. 217 (6), 2822-2840, 2008. [arXiv link]
  • Generalized Intersection Bodies, J. Func. Anal. 240 (2), 530-567, 2006. [arXiv link]
  • A comment on the low-dimensional Busemann-Petty problem, Lecture Notes in Math. 1910, GAFA Seminar Notes 2004–5, 245-253, 2007. [arXiv link]

Game Theory (M.Sc. Thesis)

  • Approachable sets of vector payoffs in stochastic games, Games and Economic Behavior 56, 135-147, 2006.
  • The semi-algebraic theory of stochastic games, Math. Oper. Research 27, 401-418, 2002.