New York University NYU Courant

Gaoyong Zhang

Professor of Mathematics
Courant Institute of Mathematical Sciences
New York University


Contact

Email address: gaoyong.zhang@nyu.edu


Research Interests

Convex Geometry, Geometric Analysis


Distinctions

Fellow of the American Mathematical Society


Education

  • Temple University, 1995
    Doctor of Philosophy, Mathematics
  • Wuhan University of Science and Technology, 1982
    Bachelor of Science, Mathematics


Selected Papers

[39] Y. Huang, E. Lutwak, D. Yang, and G. Zhang, Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems, Acta Math. 216 (2016), 325--388.

[38] A. Colesanti, K. Nystrom, P. Salani, J. Xiao, D. Yang, and G. Zhang, The Hadamard variational formula and the Minkowski problem for p-capacity, Adv. Math. 285 (2015), 1511--1588.

[37] K. J. Boroczky, E. Lutwak, D. Yang, and G. Zhang, Affine images of isotropic measures, J. Differential Geom. 99 (2015), 407--442..

[36] A. Cianchi, E. Lutwak, D. Yang, and G. Zhang, A unified approach to Cramer-Rao inequalities, IEEE Trans. Info. Theory 60 (2014), 643--650.

[35] E. Lutwak, S. Lv, D. Yang, and G. Zhang, Affine moments of a random vector, IEEE Trans. Info. Theory 59 (2013), 5592--5599.

[34] K. J. Boroczky, E. Lutwak, D. Yang, and G. Zhang, The logarithmic Minkowski problem, J. Amer. Math. Soc. 26 (2013), 831--852.

[33] K. J. Boroczky, E. Lutwak, D. Yang, and G. Zhang, The log-Brunn-Minkowski inequality, Adv. Math. 231 (2012), 1974--1997.

[32] E. Lutwak, S. Lv, D. Yang, and G. Zhang, Extensions of Fisher information and Stam's inequality, IEEE Trans. Info. Theory 58 (2012), 1319--1327.

[31] E. Lutwak, D. Yang, and G. Zhang, The Brunn-Minkowski-Firey inequality for nonconvex sets, Adv. Appl. Math. 48 (2012), 407--413.

[30] G. Bianchi, D. Klain, E. Lutwak, D. Yang, and G. Zhang, A countable set of directions is sufficient for Steiner symmetrization, Adv. Appl. Math. 47 (2011), 869--873.

[29] M. Ludwig, J. Xiao, and G. Zhang, Sharp convex Lorentz-Sobolev inequalities, Math. Ann. 350(2011), 169--197.

[28] C. Haberl, E. Lutwak, D. Yang, and G. Zhang, The even Orlicz Minkowski problem, Adv. Math. 224(2010), 2485--2510.

[27] E. Lutwak, D. Yang, and G. Zhang, Orlicz centroid bodies, J. Differential Geom. 84 (2010), 365--387.

[26] E. Lutwak, D. Yang, and G. Zhang, A volume inequality for polar bodies, J. Differential Geom. 84 (2010), 163--178.

[25] E. Lutwak, D. Yang, and G. Zhang, Orlicz projection bodies, Adv. Math. 223 (2010), 220--242.

[24] A. Cianchi, E. Lutwak, D. Yang, and G. Zhang, Affine Moser-Trudinger and Morrey-Sobolev inequalities, Calculus of Variations and PDEs 36 (2009), 419--436.

[23] E. Lutwak, D. Yang, and G. Zhang, Moment-entropy inequalities for a random vector, IEEE Trans. Info. Theory 53 (2007), 1603--1607.

[22] E. Lutwak, D. Yang, and G. Zhang, Volume inequalities for isotropic measures, Amer. J. Math. 129 (2007), 1711--1723.

[21] E. Lutwak, D. Yang, and G. Zhang, Optimal Sobolev norms and the Lp Minkowski problem, International Math. Res. Notices (2006), No. 1, 1--21.

[20] D. Hug, E. Lutwak, D. Yang, and G. Zhang, On the L_p Minkowski problem for polytopes, Discrete Comput. Geom. 33 (2005), 699--715.

[19] E. Lutwak, D. Yang, and G. Zhang, L_p John ellipsoids, Proc. London Math. Soc. 90 (2005), 497--520.

[18] E. Lutwak, D. Yang, and G. Zhang, Cramer-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information, IEEE Trans. Info. Theory 51 (2005), 473--478.

[17] E. Lutwak, D. Yang, and G. Zhang, Volume inequalities for subspaces of L_p, J. Differential Geom. 68 (2004), 159--184.

[16] B. Rubin and G. Zhang, Generalizations of the Busemann-Petty problem for sections of convex bodies, J. Funct. Anal. 213 (2004), 473--501.

[15] E. Lutwak, D. Yang, and G. Zhang, On the L_p-Minkowski problem, Trans. Amer. Math. Soc. 356 (2004), 4359-4370.

[14] E. Lutwak, D. Yang, and G. Zhang, Moment-entropy inequalities, Annals of Prob. 32 (2004), 757--774.

[13] E. Lutwak, D. Yang, and G. Zhang, Sharp affine L_p Sobolev inequalities, J. Differential Geom. 62 (2002), 17--38.

[12] E. Lutwak, D. Yang, and G. Zhang, The Cramer--Rao inequality for star bodies, Duke Math. J. 112 (2002), 59--81.

[11] E. Lutwak, D. Yang, and G. Zhang, A new affine invariant for polytopes and Schneider's projection problem, Trans. Amer. Math. Soc. 353 (2001), 1767--1779.

[10] E. Lutwak, D. Yang, and G. Zhang, L_p affine isoperimetric inequalities, J. Differential Geom. 56 (2000), 111--132.

[9] E. Lutwak, D. Yang, and G. Zhang, A new ellipsoid associated with convex bodies, Duke Math. J. 104 (2000), 375--390.

[8] J. Bourgain and Gaoyong Zhang, On a generalization of the Busemann-Petty problem, Convex geometric analysis (Berkeley, CA, 1996), 65--76, Math. Sci. Res. Inst. Publ., 34, Cambridge Univ. Press, Cambridge, 1999.

[7] E. Grinberg and Gaoyong Zhang, Convolutions, transforms, and convex bodies, Proc. London Math. Soc. 78 (1999), 77--115.

[6] Gaoyong Zhang, Dual kinematic formulas, Trans. Amer. Math. Soc. 351 (1999), 985--995.

[5] Gaoyong Zhang, A positive solution to the Busemann-Petty problem in R^4, Ann. of Math. (2) 149 (1999), 535--543.

[4] Gaoyong Zhang, The affine Sobolev inequality, J. Differential Geom. 53 (1999), 183--202.

[3] R. J. Gardner and Gaoyong Zhang, Affine inequalities and radial mean bodies, Amer. J. Math. 120 (1998), 505--528.

[2] P. Goodey and Gaoyong Zhang, Inequalities between projection functions of convex bodies, Amer. J. Math. 120 (1998), 345--367.

[1] E. Lutwak and Gaoyong Zhang, Blaschke-Santalo inequalities, J. Differential Geom. 47 (1997), 1--16.