Deane Yang

Professor, Academic Adviser

Harvard University1983

Doctor of Philosophy, Mathematics

University of Pennsylvania1979

Bachelor of Arts, Mathematics and Physics


NYU Courant Institute of Mathematical Sciences

Professor of Mathematics

From: September 2017 to present

Polytechnic University (now NYU Tandon School of Engineering)

Professor

From: September 1991 to September 2017

Columbia University

Visiting Associate Professor

From: September 1989 to May 1991

Rice University

Assistant/Associate Professor

From: January 1985 to May 1989

NYU Courant Institute of Mathematical Sciences

NSF Postdoctoral Fellow

From: September 1983 to January 1985


Journal Articles


MR3573332  Huang, Yong ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems.
Acta Math.  216  (2016),  no. 2, 325--388.
 
MR3406534  Colesanti, A. ;  Nyström, K. ;  Salani, P. ;  Xiao, J. ;  Yang, D. ;  Zhang, G.  The Hadamard variational formula and the Minkowski problem for p-capacity.
Adv. Math.  285  (2015), 1511--1588.
 
MR3316972  Böröczky, Károly J. ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Affine images of isotropic measures.
J. Differential Geom.  99  (2015),  no. 3, 407--442.
 
MR3150949  Cianchi, Andrea ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . A unified approach to Cramér-Rao inequalities.
IEEE Trans. Inform. Theory  60  (2014),  no. 1, 643--650.
 
MR3096943  Lutwak, Erwin ;  Lv, Songjun ;  Yang, Deane ;  Zhang, Gaoyong . Affine moments of a random vector.
IEEE Trans. Inform. Theory  59  (2013),  no. 9, 5592--5599.
 
MR3037788  Böröczky, Károly J. ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . The logarithmic Minkowski problem. J. Amer. Math. Soc.  26  (2013),  no. 3, 831--852.MR2964630  Böröczky, Károly J. ;  

Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . The log-Brunn-Minkowski inequality. Adv. Math.  231  (2012),  no. 3-4, 1974--1997.
 
MR2932811 (Reviewed)  Lutwak, Erwin ;  Lv, Songjun ;  Yang, Deane ;  Zhang, Gaoyong . Extensions of Fisher information and Stam's inequality. IEEE Trans. Inform. Theory  58  (2012),  no. 3, 1319--1327.
 
MR2873885 (2012m:52015)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . The Brunn-Minkowski-Firey inequality for nonconvex sets. Adv. in Appl. Math.  48  (2012),  no. 2, 407--413.
 
MR2882417 (Reviewed)  Loftin, John ;  Wang, Xu-Jia ;  Yang, Deane . Cheng and Yau's work on the Monge-Ampère equation and affine geometry. Geometry and analysis. No. 1, 163--179, Adv. Lect. Math. (ALM), 17, Int. Press, Somerville, MA,  2011.
 
MR2832382 (2012i:52008)  Bianchi, Gabriele ;  Klain, Daniel A. ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . A countable set of directions is sufficient for Steiner symmetrization. Adv. in Appl. Math.  47  (2011),  no. 4, 869--873.
   
MR2743445 (2011m:52016)  Yang, Deane . Affine integral geometry from a differentiable viewpoint. Handbook of geometric analysis, No. 2, 359--390, Adv. Lect. Math. (ALM), 13, Int. Press, Somerville, MA,  2010.
 
MR2652465 (2011g:52017)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Orlicz centroid bodies. J. Differential Geom.  84  (2010),  no. 2, 365--387.
 
MR2652213 (2011k:52006)  Haberl, Christoph ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . The even Orlicz Minkowski problem. Adv. Math.  224  (2010),  no. 6, 2485--2510.
 
MR2563216 (2011g:28008)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Orlicz projection bodies. Adv. Math.  223  (2010),  no. 1, 220--242.
 
MR2629512 (2011j:52020)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . A volume inequality for polar bodies. J. Differential Geom.  84  (2010),  no. 1, 163--178.
 
MR2551138 (2010h:46041)  Cianchi, Andrea ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Affine Moser-Trudinger and Morrey-Sobolev inequalities. Calc. Var. Partial Differential Equations  36  (2009),  no. 3, 419--436.
 
MR2369894 (2008k:52010)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Volume inequalities for isotropic measures. Amer. J. Math.  129  (2007),  no. 6, 1711--1723.
 
MR2303029 (2007m:94071)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Moment-entropy inequalities for a random vector. IEEE Trans. Inform. Theory  53  (2007),  no. 4, 1603--1607.
 
MR2240978 (2007k:60041)  Yang, Deane . Applications of information theory to convex geometry. Integral geometry and convexity, 141--151, World Sci. Publ., Hackensack, NJ,  2006.
 
MR2211138 (2007d:52007)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Optimal Sobolev norms and the Lp Minkowski problem. Int. Math. Res. Not.  2006, Art. ID 62987, 21 pp.
 
MR2236062 (2008a:94056)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Cramér-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information. IEEE Trans. Inform. Theory  51  (2005),  no. 2, 473--478.
 
MR2142136 (2006b:52007)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Lp John ellipsoids. Proc. London Math. Soc. (3)  90  (2005),  no. 2, 497--520.
 
MR2132298 (2006b:52005)  Hug, Daniel ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . On the Lp Minkowski problem for polytopes. Discrete Comput. Geom.  33  (2005),  no. 4, 699--715.
 
MR2152912 (2006j:52010)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Volume inequalities for subspaces of Lp. J. Differential Geom.  68  (2004),  no. 1, 159--184.
 
MR2111419 (2005j:52010)  Chen, W. ;  Howard, R. ;  Lutwak, E. ;  Yang, D. ;  Zhang, G.  A generalized affine isoperimetric inequality. J. Geom. Anal.  14  (2004),  no. 4, 597--612.
 
MR2106530  Kalotay, Andrew ;  Yang, Deane ;  Fabozzi, Frank J.  An option-theoretic prepayment model for mortgages and mortgage-backed
securities. Int. J. Theor. Appl. Finance  7  (2004),  no. 8, 949--978.
 
MR2067123 (2005d:52013)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . On the Lp-Minkowski problem. Trans. Amer. Math. Soc.  356  (2004),  no. 11, 4359--4370.
 
MR2039942 (2004k:60026)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Moment-entropy inequalities. Ann. Probab.  32  (2004),  no. 1B, 757--774.
 
MR1987375 (2004d:46039)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Sharp affine Lp Sobolev inequalities. J. Differential Geom.  62  (2002),  no. 1, 17--38.
 
MR1930297 (2003i:94023)  Guleryuz, Onur G. ;  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Information-theoretic inequalities for contoured probability distributions. IEEE Trans. Inform. Theory  48  (2002),  no. 8, 2377--2383.
 
MR1890647 (2003f:52006)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . The Cramer-Rao inequality for star bodies. Duke Math. J.  112  (2002),  no. 1, 59--81.
 
MR1813595 (2002c:52014)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . A new affine invariant for polytopes and Schneider's projection problem. Trans. Amer. Math. Soc.  353  (2001),  no. 5, 1767--1779.
 
MR1863023 (2002h:52011)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . Lp affine isoperimetric inequalities. J. Differential Geom.  56  (2000),  no. 1, 111--132.
 
MR1781476 (2001j:52011)  Lutwak, Erwin ;  Yang, Deane ;  Zhang, Gaoyong . A new ellipsoid associated with convex bodies. Duke Math. J.  104  (2000),  no. 3, 375--390.
 
MR1624222 (2000j:58029)  Yang, Deane . Deforming a map into a harmonic map. Trans. Amer. Math. Soc.  352  (2000),  no. 3, 1021--1038.
 
MR1264942 (95b:53051)  Rosenberg, Steven ;  Yang, Deane . Bounds on the fundamental group of a manifold with almost nonnegative Ricci curvature. J. Math. Soc. Japan  46  (1994),  no. 2, 267--287.
 
MR1169351 (93m:53037)  Yang, Deane . Convergence of Riemannian manifolds with integral bounds on curvature II. Ann. Sci. École Norm. Sup. (4)  25  (1992),  no. 2, 179--199.
 
MR1164099 (93b:53029)  Yang, Deane . Lp pinching and compactness theorems for compact Riemannian manifolds. Forum Math.  4  (1992),  no. 3, 323--333.
 
MR1154180 (93e:53052)  Yang, Deane . Riemannian manifolds with small integral norm of curvature. Duke Math. J.  65  (1992),  no. 3, 501--510.
 
MR1152614 (93a:53037)  Yang, Deane . Convergence of Riemannian manifolds with integral bounds on curvature I. Ann. Sci. École Norm. Sup. (4)  25  (1992),  no. 1, 77--105.
 
MR1052910 (92k:53073)  Smith, P. D. ;  Yang, Deane . Removing point singularities of Riemannian manifolds. Trans. Amer. Math. Soc.  333  (1992),  no. 1, 203--219.
 
MR1104838 (92f:58039)  Yang, Deane . Existence and regularity of energy-minimizing Riemannian metrics. Internat. Math. Res. Notices  1991,  no. 2, 7--13.
 
MR0982180 (91f:53065)  Chow, Bennett ;  Yang, Deane . Rigidity of nonnegatively curved compact quaternionic-Kähler manifolds. J. Differential Geom.  29  (1989),  no. 2, 361--372.
 
MR1046260 (91k:53056)  Yang, Deane . Lp pinching and compactness theorems for compact Riemannian manifolds. Séminaire de Théorie Spectrale et Géométrie, No. 6, Année 1987–1988, 81--89, Univ. Grenoble I, Saint-Martin-d'Hères,  1988.
 
MR0897707 (89b:58232)  Yang, Deane . Involutive hyperbolic differential systems. Mem. Amer. Math. Soc.  68  (1987),  no. 370, xii+93 pp.
 
MR0848931 (87j:53059)  DeTurck, Dennis ;  Yang, Deane . Local existence of smooth metrics with prescribed curvature. Nonlinear problems in geometry (Mobile, Ala., 1985), 37--43, Contemp. Math., 51, Amer. Math. Soc., Providence, RI,  1986.
 
MR0829847 (87h:58202)  Yang, Deane . Local solvability of overdetermined systems defined by commuting
first-order differential operators.
Comm. Pure Appl. Math.  39  (1986),  no. 3, 401--421.
 
MR0747867 (86b:73014)  DeTurck, Dennis M. ;  Yang, Deane . Existence of elastic deformations with prescribed principal strains and triply orthogonal systems. Duke Math. J.  51  (1984),  no. 2, 243--260.
 
MR0726313 (85d:53027)  Bryant, Robert L. ;  Griffiths, Phillip A. ;  Yang, Deane . Characteristics and existence of isometric embeddings. Duke Math. J.  50  (1983),  no. 4, 893--994.

See my personal homepage



Research Interests


Convex geometric analysis, Riemannian geometry, Partial differential equations



  • Sloan Foundation Fellow, 1998-1990
  • Inaugural AMS Fellow, 2012