## Contact

Email: gaoyong.zhang@nyu.edu

Office: WWH 523; 2MTC 852

## Research Interests

Convex Geometry, Geometric Analysis

## Distinctions

Fellow of the American Mathematical Society

## Education

- Doctor of Philosophy, Mathematics

Temple University, 1995 - Bachelor of Science, Mathematics

Wuhan University of Science and Technology, 1982

## Professional Experience

**New York University**

Professor

January 2014 to present**Polytechnic University**

Professor

September 2000 to December 2013**Polytechnic University**

Assistant Professor

September 1997 to August 2000**University of Pennsylvania**

Rademacher Lecturer

September 1995 to July 1997**Institute for Advanced Study**

Member

January 1996 to August 1996**Wuhan University of Science and Technology**

Lecturer

September 1986 to August 1991

## Selected Papers

[42] K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang, Y. Zhao, The dual Minkowski problem for symmetric convex bodies, **Adv. Math.** 356 (2019), 106805.

[41] Y. Huang, E. Lutwak, D. Yang, G. Zhang, The L_p-Aleksandrov problem for L_p-integral curvature, **J. Differential Geom.** 110 (2018), no. 1, 1--29.

[41] E. Lutwak, D. Yang, G. Zhang, L_p dual curvature measures, **Adv. Math.** 329 (2018), 85--132.

[40] A. Li, D. Xi, G. Zhang, Volume inequalities of convex bodies from cosine transforms on Grassmann manifolds, **Adv. Math.** 304 (2017), 494--538.

[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.