Gaoyong   Zhang

Gaoyong Zhang

Professor

Mathematics

Journal Articles

 

  • A. Cianchi, E. Lutwak, D. Yang, and G. Zhang, A unified approach to Cramer-Rao inequalities, IEEE Trans. Info. Theory (2013) (accepted for publication).
  • E. Lutwak, S. Lv, D. Yang, and G. Zhang, Affine moments of a random vector, IEEE Trans. Info. Theory (2013) (accepted for publication). 
  • K.J. Boroczky, E. Lutwak, D. Yang, and G. Zhang, The logarithmic Minkowski problem, Journal of AMS, 26 (2013), 831-852.
  • K.J. Boroczky, E. Lutwak, D. Yang, and G. Zhang, The log-Brunn-Minkowski inequality, Adv. Math. 231 (2012), 1974--1997.
  • E. Lutwak, S. Lv, D. Yang, and Zhang, Extensions of Fisher information and Stam's inequality, IEEE Trans. Info. Theory 58 (2012), 1319--1327.
  • E. Lutwak, D. Yang, and G. Zhang, The Brunn-Minkowski-Firey inequality for nonconvex sets, Adv. Appl. Math. 48 (2012), 407--413.
  • 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.
  • M. Ludwig, J. Xiao, and G. Zhang, Sharp convex Lorentz-Sobolev inequalities, Math. Ann. 350 (2011), 169--197.
  • C. Haberl, E. Lutwak, D. Yang, and G. Zhang, The even Orlicz Minkowski problem, Adv. Math. 224 (2010), 2485--2510.
  • E. Lutwak, D. Yang, and G. Zhang, Orlicz centroid bodies, J. Differential Geom. 84 (2010), 365--387.
  • E. Lutwak, D. Yang, and G. Zhang, A volume inequality for polar bodies, J. Differential Geom. 84 (2010), 163--178.
  • E. Lutwak, D. Yang, and G. Zhang, Orlicz projection bodies, Adv. Math. 223 (2010), 220--242.
  • 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.
  • E. Lutwak, D. Yang, G. Zhang, Moment-entropy inequalities for a random vector, IEEE Trans. Info. Theory 53 (2007), 1603--1607.
  • E. Lutwak, D. Yang, G. Zhang, Volume inequalities for isotropic measures, Amer. J. Math. 129 (2007), 1711--1723.
  • E. Lutwak, D. Yang, G. Zhang, Optimal Sobolev norms and the Lp Minkowski problem, International Math. Res. Notices, (2006), No. 1, 1--21.
  • D. Hug, E. Lutwak, D. Yang, and G. Zhang, On the L_p Minkowski problem for polytopes, Discrete Comput. Geom. 33 (2005), 699--715.
  • E. Lutwak, D. Yang, and G. Zhang, L_p John ellipsoids, Proc. London Math. Soc. 90 (2005), 497--520.
  • 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.
  • E. Lutwak, D. Yang, and G. Zhang, Volume inequalities for subspaces of L_p, J. Differential Geom. 68 (2004), 159--184.
  • B. Rubin and G. Zhang, Generalizations of the Busemann-Petty problem for sections of convex bodies, J. Funct. Anal. 213 (2004), 473--501.
  • E. Lutwak, D. Yang, and G. Zhang, On the L_p-Minkowski problem, Trans. Amer. Math. Soc. 356 (2004), 4359-4370.
  • E. Lutwak, D. Yang, and G. Zhang, Moment-entropy inequalities, Annals of Prob. 32 (2004), 757--774.
  • E. Lutwak, D. Yang, and G. Zhang, Sharp affine L_p Sobolev inequalities, J. Differential Geom. 62 (2002), 17--38.
  • E. Lutwak, D. Yang, and G. Zhang, The Cramer--Rao inequality for star bodies, Duke Math. J. 112 (2002), 59--81.
  • 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.
  • E. Lutwak, D. Yang, and G. Zhang, L_p affine isoperimetric inequalities, J. Differential Geom. 56 (2000), 111--132.
  • E. Lutwak, D. Yang, and G. Zhang, A new ellipsoid associated with convex bodies, Duke Math. J. 104 (2000), 375--390.
  • 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.
  • E. Grinberg and Gaoyong Zhang, Convolutions, transforms, and convex bodies, Proc. London Math. Soc. 78 (1999), 77--115.
  • Gaoyong Zhang, Dual kinematic formulas. Trans. Amer. Math. Soc. 351 (1999), 985--995.
  • Gaoyong Zhang, A positive solution to the Busemann-Petty problem in R^4, Ann. of Math. (2) 149 (1999), 535--543.
  • Gaoyong Zhang, The affine Sobolev inequality, J. Differential Geom. 53(1999), 183--202.
  • R. J. Gardner and Gaoyong Zhang, Affine inequalities and radial mean bodies, Amer. J. Math. 120 (1998), 505--528.
  • P. Goodey and Gaoyong Zhang, Inequalities between projection functions of convex bodies, Amer. J. Math. 120 (1998), 345--367.
  • E. Lutwak and Gaoyong Zhang, Blaschke-Santalo inequalities, J. Differential Geom. 47 (1997), 1--16.

Education

Temple University, Class of 1995

Doctor of Philosophy, Mathematics

Wuhan University of Science and Technology, Wuhan University, Class of 1986

Master of Science, Mathematics

Wuhan University of Sci & Tech, Wuhan University of Technology, Class of 1982

Bachelor of Science, Mathematics

Experience

Polytechnic Institute of New York University

Professor

From: October 2000 to present

Polytechnic Institute of New York University

Assistant Professor

From: October 1997 to August 2000

University of Pennsylvania

Rademacher Lecturer

From: October 1995 to July 1997

Institute for Advanced Study

Member

From: January 1996 to August 1996

Wuhan University of Science and Technology

Lecturer

From: October 1986 to August 1991

Awards + Distinctions

Fellow of the American Mathematical Society

Research Interests

Convex geometry  

Geometric analysis

Integral geometry