Publications

Forthcoming
Giannopoulos A, Koldobsky A, Zvavitch A. Inequalities for the Radon transform on convex sets. International Mathematics Research Notices [Internet]. Forthcoming. Publisher's Version radon-comparison.pdf
2022
Brazitikos, S.; Giannopoulos A. Continuous version of the approximate geometric Brascamp-Lieb inequalities. Journal of Geometric Analysis [Internet]. 2022;32(6). Publisher's Version bl_continuous.pdf
2021
Artstein-Avidan S, Giannopoulos A, Milman V. Asymptotic Geometric Analysis, Part II. Providence, RI: American Mathematical Society (Mathematical Surveys and Monographs, vol. 261); 2021 pp. xxxvii+645. Publisher's Version
2020
Chasapis G, Giannopoulos A, Skarmogiannis N. Norms of weighted sums of log-concave random vectors. Communications in Contemporary Mathematics [Internet]. 2020;22(4). Publisher's Version reverse-gm.pdf
2018
Giannopoulos A, Koldobsky A, Valettas P. Inequalities for the surface area of projections of convex bodies. Canadian Journal of Mathematics [Internet]. 2018;70:804-823. Publisher's Version
Brazitikos S, Giannopoulos A, Liakopoulos D-M. Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies. Advances in Geometry [Internet]. 2018;18:345-354. Publisher's Version lw-restricted.pdf
Giannopoulos A, Koldobsky A. Volume difference inequalities. Transactions of the American Mathematical Society [Internet]. 2018;370:4351-4372. Publisher's Version volume-difference.pdf
2017
Chasapis G, Giannopoulos A, Liakopoulos D-M. Estimates for measures of lower dimensional sections of convex bodies. Advances in Mathematics [Internet]. 2017;306:880-904. Publisher's Version
Brazitikos S, Dann S, Giannopoulos A, Koldobsky A. On the average volume of sections of convex bodies. Israel Journal of Mathematics [Internet]. 2017;222:921-947. Publisher's Version average-sections.pdf
Giannopoulos A, Koldobsky A. Variants of the Busemann-Petty problem and of the Shephard problem. International Mathematics Research Notices [Internet]. 2017;(3):921-943. Publisher's Version
2016
Giannopoulos A, Hioni L, Tsolomitis A. Asymptotic shape of the convex hull of isotropic log-concave random vectors. Advances in Applied Mathematics [Internet]. 2016;75:116-143. Publisher's Version
Chasapis G, Giannopoulos A. Euclidean regularization in John's position. Indiana University Mathematics Journal [Internet]. 2016;65:1877-1890. Publisher's Version
Giannopoulos A, Hioni L, Tsolomitis A. Geometry of random sections of isotropic convex bodies. Bulletin of the Hellenic Mathematical Society [Internet]. 2016;60:20-40. Publisher's Version
Giannopoulos A, Markessinis E, Tsolomitis A. Remarks on an inequality of Rogers and Shephard. Proceedings of the American Mathematical Society [Internet]. 2016;144:763-773. Publisher's Version
2015
Artstein-Avidan S, Giannopoulos A, Milman V. Asymptotic Geometric Analysis, Part I. Providence, RI: American Mathematical Society (Mathematical Surveys and Monographs, Vol. 202); 2015 pp. xx+451. Publisher's Version
Giannopoulos A, Stavrakakis P, Tsolomitis A, Vritsiou B-H. Geometry of the L_q centroid bodies of an isotropic log-concave measure. Transactions of the American Mathematical Society [Internet]. 2015;367:4569-4593. Publisher's Version
2014
Brazitikos S, Giannopoulos A, Valettas P, Vritsiou B-H. Geometry of Isotropic Convex Bodies. Providence - RI: Mathematical Surveys and Monographs, 196. American Mathematical Society; 2014 pp. xx+594. Publisher's Version
Giannopoulos A, Paouris G, Vritsiou B-H. The isotropic position and the reverse Santalo inequality. Israel Journal of Mathematics [Internet]. 2014;203:1-22. Publisher's Version
Giannopoulos A, Milman E. M-estimates for isotropic convex bodies and their L_q centroid bodies. In: Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics . Vol. 2116. ; 2014. pp. 159-182. Publisher's Version
2013
Dafnis N, Giannopoulos A, Tsolomitis A. Quermassintegrals and asymptotic shape of random polytopes in an isotropic convex body. Michigan Mathematical Journal [Internet]. 2013;62:59-79. Publisher's Version
2012
Giannopoulos A, Paouris G, Vritsiou B-H. A remark on the slicing problem. Journal of Functional Analysis [Internet]. 2012;262:1062-1086. Publisher's Version
Giannopoulos A, Paouris G, Valettas P. On the distribution of the psi(2)-norm of linear functionals on isotropic convex bodies. In: Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics. Vol. 2050. Heidelberg: Springer; 2012. pp. 227-253. Publisher's Version
Giannopoulos A, Paouris G, Valettas P. Psi(a)-estimates for marginals of log-concave probability measures. Proceedings of the American Mathematical Society [Internet]. 2012;140:1297-1308. Publisher's Version
2011
Giannopoulos A, Paouris G, Valettas P. On the existence of subgaussian directions for log-concave measures. In: Concentration, Functional Inequalities and Isoperimetry, Contemporary Mathematics. Vol. 545. Providence -RI: American Mathematical Society; 2011. pp. 103-122. Publisher's Version
2010
Dafnis N, Giannopoulos A, Guedon O. On the isotropic constant of random polytopes. Advances in Geometry [Internet]. 2010;10:311-321. Publisher's Version
2009
Dafnis N, Giannopoulos A, Tsolomitis A. Asymptotic shape of a random polytope in a convex body. Journal of Functional Analysis [Internet]. 2009;257:2820-2839. Publisher's Version
Gatzouras D, Giannopoulos A. Threshold for the volume spanned by random points with independent coordinates. Israel Journal of Mathematics [Internet]. 2009;169:125-153. Publisher's Version
2007
Giannopoulos A, Pajor A, Paouris G. A note on subgaussian estimates for linear functionals on convex bodies. Proceedings of the American Mathematical Society [Internet]. 2007;135:2599-2606. Publisher's Version
Gatzouras D, Giannopoulos A, Markoulakis N. On the maximal number of facets of 0/1 polytopes. In: Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics. Vol. 1910. Berlin: Springer; 2007. pp. 117-125. Publisher's Version
2006
Gatzouras D, Giannopoulos A. A large deviations approach to the geometry of random polytopes. Mathematika [Internet]. 2006;53:173-211. Publisher's Version
2005
Giannopoulos A, Milman V, Tsolomitis A. Asymptotic formulas for the diameter of sections of symmetric convex bodies. Journal of Functional Analysis [Internet]. 2005;223:86-108. Publisher's Version
Gatzouras D, Giannopoulos A, Markoulakis N. Lower bound for the maximal number of facets of a 0/1 polytope. Discrete and Computational Geometry [Internet]. 2005;34:331-349. Publisher's Version
Giannopoulos A, Hartzoulaki M, Tsolomitis A. Random points in isotropic unconditional convex bodies. Journal of the London Mathematical Society [Internet]. 2005;72:779-798. Publisher's Version
2004
Giannopoulos A, Milman V. Asymptotic convex geometry short overview. In: Different Faces of Geometry, International Mathematical Series. Vol. 3. New York: Kluwer/Plenum; 2004. pp. 87-162. Publisher's Version
2003
Fradelizi M, Giannopoulos A, Meyer M. Some inequalities about mixed volumes. Israel Journal of Mathematics [Internet]. 2003;135:157-179. Publisher's Version
Giannopoulos A, Tsolomitis A. Volume radius of a random polytope in a convex body. Mathematical Proceedings of the Cambridge Philosophical Society [Internet]. 2003;134:13-21. Publisher's Version
2002
Giannopoulos A, Hartzoulaki M. Random spaces generated by vertices of the cube. Discrete and Computational Geometry [Internet]. 2002;28:255-273. Publisher's Version
Giannopoulos A, Hartzoulaki M, Paouris G. On a local version of the Aleksandrov-Fenchel inequalities for the quermassintegrals of a convex body. Proceedings of the American Mathematical Society [Internet]. 2002;130:2403-2412. Publisher's Version
Giannopoulos A, Hartzoulaki M. On the volume ratio of two convex bodies. Bulletin of the London Mathematical Society [Internet]. 2002;34:703-707. Publisher's Version
2001
Giannopoulos A, Milman V. Euclidean structure in finite dimensional spaces. In: Handbook of the Geometry of Banach Spaces . Vol. 1. Amsterdam: North-Holland; 2001. pp. 707-779. Publisher's Version
Giannopoulos A, Perissinaki E, Tsolomitis A. John's theorem for an arbitrary pair of convex bodies. Geometriae Dedicata [Internet]. 2001;84:63-79. Publisher's Version
2000
Giannopoulos A, Milman V. Concentration property on probability spaces. Advances in Mathematics [Internet]. 2000;156:77-106. Publisher's Version
Giannopoulos A, Milman V, Rudelson M. Convex bodies with minimal mean width . In: Geometric Aspects of Functional Analysis, Lecture Notes in Mathematics. Vol. 1745. Berlin: Springer; 2000. pp. 81-93. Publisher's Version
Giannopoulos A, Milman V. Extremal problems and isotropic positions of convex bodies. Israel Journal of Mathematics [Internet]. 2000;117:29-60. Publisher's Version
1999
Giannopoulos A, Papadimitrakis M. Isotropic surface area measures. Mathematika [Internet]. 1999;46:1-13. Publisher's Version
Gardner R, Giannopoulos A. p-Cross-section bodies. Indiana Univ. Math. J. [Internet]. 1999;48:593-614. Publisher's Version
1998
Giannopoulos A, Milman V. Mean width and diameter of proportional sections of a symmetric convex body . J. Reine Angew. Math. [Internet]. 1998;497:113-139. Publisher's Version
1997
Giannopoulos A, Milman V. How small can the intersection of a few rotations of a symmetric convex body be? . C.R. Acad. Sci. Paris [Internet]. 1997;325:389-394. Publisher's Version
Giannopoulos A, Milman V. Low M*-estimates on coordinate subspaces. Journal of Functional Analysis [Internet]. 1997;147:457-484. Publisher's Version
Giannopoulos A. On some vector balancing problems. Studia Mathematica [Internet]. 1997;122:225-234. Publisher's Version
Giannopoulos A, Milman V. On the diameter of proportional sections of a symmetric convex body. International Mathematics Research Notices [Internet]. 1997;(1):5-19. Publisher's Version
1996
Giannopoulos A. A proportional Dvoretzky-Rogers factorisation result. Proceedings of the American Mathematical Society [Internet]. 1996;124:233-241. Publisher's Version
1995
Giannopoulos A. A note on the Banach-Mazur distance to the cube. In: Operator Theory: Advances and Applications. Vol. 77. Basel: Birkhauser; 1995. pp. 67-73. Publisher's Version
1992
Giannopoulos A. On the mean value of the area of a random polygon in a plane convex body. Mathematika [Internet]. 1992;39:279-290. Publisher's Version