Convex Geometry and Local Theory of Normed Spaces

• An ``isomorphic" version of Dvoretzky's theorem (with V.D. Milman), C. R. Acad. Sci. Paris t. 321 S\'erie I, (1995), 541--544.
• Global vs. local asymptotic theories of finite dimensional normed spaces (with V.D. Milman), Duke Math. J. 90 (1997), 73--93.
• An ``isomorphic" version of Dvoretzky's theorem II (with V.D. Milman), Convex geometric analysis (Berkeley, CA, 1996), Math. Sci. Res. Inst. Publ., 34, Cambridge Univ. Press, Cambridge, (1999).
• Averages of norms and behavior of families of projective caps on the sphere (with A.E. Litvak and V.D. Milman), C. R. Acad. Sci. Paris t. 325 S\'erie I, (1997), 289--294.
• Averages of norms and quasi-norms (with A.E. Litvak and V.D. Milman), Math. Annalen 312 (1998), 95--124.
• Embedding subspaces of $L_p$ into $\ell^N_p$, $0<p<1$ (with A. Zvavitch), Math. Nachr. 227 (2001), 133--142.
• Concentration, results and applications, in preparation for handbook, preliminary version available.
• Finite dimensional subspaces of $L_p$ (with W.B. Johnson), Handbook of the Geometry of Banach Spaces, Vol 1, W.B. Johnson and J. Lindenstrauss, eds, Elsevier, Amsterdam (2001), 837--870.
• Concentration on the $\ell_p^n$ ball (with J. Zinn), GAFA Seminar 1996-2000, Lecture Notes in Math., Vol. 1745, pp. 245--256, Springer (2000).
• An editorial comment on the preceding paper, GAFA Seminar 1996-2000, Lecture Notes in Math., Vol. 1745, pp. 19--20, Springer (2000).
• Maximal $\ell_p^n$-structures in spaces with extremal parameters (with N. Tomczak-Jaegermann and R. Vershynin), GAFA Seminar 2001-2002, Lecture Notes in Math., Vol 1807,  (2003).
• Very tight embeddings of subspaces of $L_p$, $1\le p<2$, into $\ell_p^n$ (with W.B. Johnson ), Geometric and Funct. Anal., 13 (2003), 845--851.
• Special orthogonal splittings of $L_1^{2k}$, Israel J. Math. 139 (2004).
• Several remarks concerning the local theory of $L_p$ spaces (with W.B. Johnson), GAFA Seminar 2002-2003, 139--148, Lecture Notes in Math., Vol 1850, (2004).
• Two observations regarding embedding subsets of Euclidean spaces in normed spaces, Advances in Mathematics 200 (2006) 125--135.
• The random version of Dvoretzky's theorem in $\ell_\infty^n$, GAFA Seminar 2004-2005, 265—270, Lecture Notes in Math., Vol 1910, Springer-Verlag (2007).
• Lower bounds for local versions of dimension reductions (with Adi Shraibman), Discrete Comput. Geom. 41 (2009), no. 2, 273--283.
• Diamond graphs and super-reflexivity (with W.B. Johnson), J. Topol. Anal. 1 (2009), no. 2, 177--189.
• Tight embedding of subspaces of $L_p$ in $\ell_p^n$ for even $p$, Proc. AMS, Proc. AMS, 139 (2011), no. 12, 4419–4421.
• Approximate Gaussian isoperimetry for $k$ sets, to appear.
• Commutators on $\L_p$, $1\leq p <\infty$ (with D. Dosev and W.B. Johnson), to appear.
• Approximate Gaussian isoperimetry for $k$ sets, to appear.
• Dimension Reduction in $L_p$, $0<p<2$, was not sent for publication.
• Bourgain's discretization Theorem, (with O. Gilady and A. Naor), to appear
• Euclidean sections of convex bodies, series of lectures given in Bedlewo, Poland, July 6-12, 2008 and in Kent, Ohio, August 13-20, 2008, was not sent for publication.
• A quantitative version of the commutator theorem for zero trace matrices, (with W.J. Johnson and N. Ozawa), to appear