Articles and preprints

  1. Sections of convex bodies through their centroid, Archiv der Mathematik 69 (1997), 515-522.
  2. Hyperplane sections of convex bodies in isotropic position, Beiträge zur Algebra und Geometrie 40 (1999), No. 1, 163-183.
  3. A short solution to the Busemann-Petty problem, Positivity 3 (1999), 95-100 (with Franck Barthe and Bernard Maurey)
  4. Sectional bodies associated to a convex body, Proceedings of the American Mathematical Society 128 (2000), No. 9, 2735-2744.
  5. Shift inequalities of Gaussian type and norms of barycenters, Studia Mathematica 146 (2001), 245-259 (with Franck Barthe and Dario Cordero-Erausquin).
  6. Some inequalities about mixed volumes, Israel Journal of Mathematics 135 (2003), 157-179 (with Apostolos Giannopoulos and Mathieu Meyer).
  7. The (B)-conjecture for the Gaussian measure of dilates of symmetric convex sets and related problems, Journal of Functional Analysis 214 (2004), 410-427 (with Dario Cordero-Erausquin and Bernard Maurey).
  8. Two-point symmetrization and convexity, Archiv der Mathematik 82 (2004), 282-288 (with Guillaume Aubrun).
  9. The extreme points of subsets of s-concave probabilies and a geometric localization theorem, Discrete and Computational Geometry 31 (2004), 327-335 (with Olivier Guédon).
  10. A generalized localization theorem and geometric inequalities for convex bodies, Advances in Mathematics 204 (2006), 509-529 (with Olivier Guédon).
  11. Some functional forms of Blaschke-Santaló inequality, Mathematische Zeitschrift 256 (2007), 379-395 (with Mathieu Meyer).
  12. Some functional inverse Santaló inequalities, Advances in Mathematics 218 (2008), 1430-1452 (with Mathieu Meyer).
  13. Increasing functions and inverse Santaló inequality for unconditional functions, Positivity 12 (2008), 407-420 (with Mathieu Meyer).
  14. Concentration inequalities for s-concave measures of dilations of Borel sets and applications, Electronic Journal of Probability Vol. 14 (2009), Paper no. 71, 2068-2090.
  15. The case of equality for an inverse Santaló functional inequality, Advances in Geometry 10 (2010), 621--630 (with Yehoram Gordon, Mathieu Meyer and Shlomo Reisner).
  16. Functional inequalities related to Mahler conjecture, Monatshefte für Mathematik 159, No. 1-2 (2010), 13-25 (with Mathieu Meyer).
  17. An application of shadow systems to Mahler's conjecture, Discrete and Computational Geometry 48 (2012), no. 3, 721-734 (with Mathieu Meyer and Artem Zvavitch).
  18. Simplices in the Euclidean ball, Canadian Mathematical Bulletin 55 (2012), 498-508 (with Grigoris Paouris and Carsten Schütt).
  19. The volume product of convex bodies with many hyperplane symmetries, American Journal of Mathematics 135 (2013), 1-37 (with Franck Barthe).
  20. Stability of the functional forms of the Blaschke-Santaló inequality, Monatshefte für Mathematik 173 (2014), 135-159, (with Franck Barthe and Karoly Böröczky Jr.).
  21. On the analogue of the concavity of entropy power in the Brunn-Minkowski theory, Advances in Applied Mathematics 57 (2014), 1-20, (with Arnaud Marsiglietti).
  22. Thin-shell concentration for convex measures, Studia Mathematica 223 (2) (2014), 123-148, (with Olivier Guédon and Alain Pajor).
  23. Volume of the polar of random sets and shadow systems, Mathematische Annalen 362 (2015), 1305-1325, (with Dario Cordero-Erausquin, Grigoris Paouris and Peter Pivovarov).
  24. Functional versions of $L_p$-affine surface area and entropy inequalities, International Mathematics Research Notices (2016) Vol. 2016, 1223-1250, doi: 10.1093/imrn/rnv151, (with Umut Caglar, Olivier Guédon, Joseph Lehec, Carsten Schütt and Elisabeth Werner).
  25. Do Minkowski averages get progressively more convex?, C. R. Acad. Sci. Paris, Ser. I 354 (2016) 185-189, (with Mokshay Madiman, Arnaud Marsiglietti and Artem Zvavitch).
  26. Optimal Concentration of Information Content For Log-Concave Densities, High Dimensional Probability VII, The Cargèse Volume, Progress in Probability 71, Birkhauser (2016), 45-60, (with Mokshay Madiman and Liyao Wang).
  27. On the volume of sections of a convex body by cones, Proceedings of the American Mathematical Society 145 (7) (2017), 3153-3164 (with Mathieu Meyer and Vlad Yaskin).
  28. The convexification effect of Minkowski summation, EMS Surveys in Mathematical Sciences 5 (2018), 1-64, (with Mokshay Madiman, Arnaud Marsiglietti and Artem Zvavitch).
  29. Polytopes of Maximal Volume Product, Discrete and Computational Geometry 62 (3) (2019), 583-600, DOI 10.1007/s00454-019-00072-3, (with Matthew Alexander and Artem Zvavitch).
  30. Concentration of information content for convex measures, expanded version (from 5 to 22 pages) of the conference version. Electronic Journal of Probability, 25 (2020) paper no. 20, 22 pp. (with Jiange Li and Mokshay Madiman).
  31. Random polytopes and the wet part for arbitrary probability distributions. Annales Henri Lebesgue, Vol. 3 (2020), pp. 701-715, (with Imre Bárány, Xavier Goaoc, Alfredo Hubard and Günter Rote)
  32. Geometry and volume product of finite dimensional Lipschitz-free spaces, Journal of Functional Analysis 280 (2021) 108849 (with Matthew Alexander, Luis Carlos Garcia-Lirola and Artem Zvavitch).
  33. Equipartitions and Mahler volume of symmetric convex bodies, (with Alfredo Hubard, Mathieu Meyer, Edgardo Roldán-Pensado and Artem Zvavitch). To appear in American Journal of Mathematics. Preprint July 2019.
  34. Volume of the Minkowski sums of star-shaped sets, (with Zsolt Lángi and Artem Zvavitch). Submitted. Preprint October 2019.
  35. The functional form of Mahler conjecture for even log-concave functions in dimension 2, (with Elie Nakhle). Submitted. Preprint January 2021.

Refereed conference publication

  1. Concentration of information content for convex measures, Proceedings of the 2016 IEEE International Symposium on Information Theory (ISIT), 1128-1132. DOI: 10.1109/ISIT.2016.7541475. (with Jiange Li and Mokshay Madiman).
  2. Usable deviation bounds for the information content of convex measures, 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 2020, pp. 2258-2263. (with Jiange Li and Mokshay Madiman).