Deane Yang
Professor of Mathematics
email: deane.yang@courant.nyu.edu
office: Rogers Hall 305A (Brooklyn)
Teaching (Fall 2017)
MAUY 1002 The Art of Mathematics (registered students only)
MAUY 2114 Multivariable Calculus (registered students only)
Research
I work with Erwin Lutwak and Gaoyong Zhang on affine and linearly
invariant geometric and analytic inequalities. In the past I have
worked on overdetermined systems of PDE's and convergence and
collapsing theorems for Riemannian manifolds.
Academic profiles
Google Scholar
Mathscinet (requires university or individual subscription)
Professional history

2017—present: Professor of Mathematics, NYU Courant Institute of Mathematical Sciences
 1993—2017: Professor of Mathematics, NYU Tandon School of Engineering (formerly known as Polytechnic University)
 1996—1997: Vice Provost for Academic Development, Polytechnic University
 1993—1995: Department Head of Mathematics, Polytechnic University
 1991—1993: Associate Professor, Polytechnic University
 1989—1991: Visiting Associate Professor, Columbia University
 1988—1990: Associate Professor, Rice University
 1985—1988: Assistant Professor, Rice University
 1983—1984: NSF Postdoctoral Fellow, NYU Courant Institute of Mathematical Sciences
 1983: PhD in Mathematics, Harvard University
 1979: BA in Mathematics and Physics, University of Pennsylvania
Survey papers
 D. Yang, Affine
Integral Geometry from a Differentiable Viewpoint,
Handbook of
Geometric Analysis vol. II, International Press, 2010.
 J. Loftin, X. J. Wang, D. Yang,
Cheng and Yau's work on the MongeAmpère
equation and affine geometry,
Geometry and Analysis (Vol. I), Higher Education Press and International Press, 2010.
 D. Yang,
On Wilhelm Blaschke's Mathematical Work and Influence on
S. S. Chern
(Chinese version).
Selected refereed journal articles
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copyright holders.
 E. Lutwak, D. Yang, G. Zhang.
A
new ellipsoid associated with convex bodies, Duke
Mathematical Journal 104 (2000) 375390.
 E. Lutwak, D. Yang, G. Zhang.
L_{p}
affine isoperimetric inequalities, Journal of Differential
Geometry 56 (2000) 111132.
 E. Lutwak, D. Yang, G. Zhang. A
new affine invariant for polytopes and Schneider's projection
problem. Transactions of the AMS 353 (2001)
17671779.
 O. Guleryuz, E. Lutwak, D. Yang, G. Zhang. Information
theoretic inequalities for contoured probability
distributions, IEEE Transactions on Information Theory
48 (2002) 23772383.
 E. Lutwak, D. Yang, G. Zhang. The
CramerRao inequality for star bodies, Duke Mathematical
Journal 112 (2002) 5981.
 E. Lutwak, D. Yang, G. Zhang. Sharp
affine L_{p} Sobolev Inequalities, Journal of
Differential Geometry 62 (2002) 1738.
 E. Lutwak, D. Yang, G. Zhang. Momententropy
inequalities, Annals of Probability 32 (2004)
757774.
 E. Lutwak, D. Yang, G. Zhang. On
the L_{p}Minkowski problem, Transactions of
the AMS 356 (2004) 43594370.
 D. Hug, E. Lutwak, D. Yang, and G. Zhang, On
the L_{p} Minkowski problem for polytopes, Discrete
and Computational Geometry (2005) 699715.
 E. Lutwak, D. Yang, and G. Zhang, L_{p}
John ellipsoids, Proceedings of the London Mathematical
Society 90 (2005) 497520.
 E. Lutwak, D. Yang, and G. Zhang, Volume
inequalities for subspaces of L_{p}, Journal of
Differential Geometry 68 (2004) 159184.
 W. Chen, R. Howard, E. Lutwak, D. Yang, and G. Zhang, A
generalized affine isoperimetric inequality, Journal of
Geometric Analysis 14 (2004) 597612.
 E. Lutwak, D. Yang, G. Zhang. CramerRao
and momententropy inequalities for Renyi entropy and generalized
Fisher information, IEEE Transactions on Information Theory
51 (2005) 473478.
 E. Lutwak, D. Yang, G. Zhang. Optimal
Sobolev Norms and the L_{p} Minkowski
Problem, International Mathematical Research Notices
(2006) 121.
 E. Lutwak, D. Yang, G. Zhang. Volume
Inequalities for Isotropic Measures, American Journal of
Mathematics 129 (2007) 17111723.
 E. Lutwak, D. Yang, G. Zhang. Momententropy
inequalities for a random vector, IEEE Transactions on
Information Theory 53 (2007) 16031607.
 A. Cianchi, E. Lutwak, D. Yang, G. Zhang.
Affine MoserTrudinger and
MorreySobolev inequalities, Calculus of Variations and
PDE's 36 (2009) 419436.

E. Lutwak, D. Yang, G. Zhang.
Orlicz projection bodies,
Advances in Mathematics 223 (2010) 220242.

C. Haberl, E. Lutwak, D. Yang, G. Zhang.
The
even Orlicz Minkowski problem,
Advances in Mathematics 224 (2010) 24852510.

E. Lutwak, D. Yang, G. Zhang.
A volume inequality for polar bodies,
Journal of Differential Geometry 84 (2010) 163178.

E. Lutwak, D. Yang, G. Zhang.
Orlicz centroid bodies,
Journal of Differential Geometry 84 (2010) 365387.

G. Bianchi, D. Klain, E. Lutwak, D. Yang, G. Zhang.
A countable set of directions is sufficient for Steiner symmetrization,
Advances in Applied Mathematics 47 (2011) 869873.

E. Lutwak, D. Yang, G. Zhang.
The BrunnMinkowskiFirey inequality for nonconvex sets,
Advances in Applied Mathematics 48 (2012) 407413.

E. Lutwak, S. Lv, D. Yang, G. Zhang.
Extensions of Fisher information and Stam's inequality,
IEEE Transactions in Information Theory (2012) 13191327.

K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang.
The logBrunnMinkowski inequality,
Advances in Mathematics 231 (2012) 19741997.

K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang.
The logarithmic Minkowski problem,
Journal of the American Mathematics Society 26 (2013) 831852.

E. Lutwak, S Lv, D. Yang, G. Zhang.
Affine moments of a random vector,
IEEE Transactions in Information Theory 59
(2013) 55925599

A. Cianchi, E. Lutwak, D. Yang, G. Zhang.
A Unified Approach to CramérRao Inequalities,
IEEE Transactions in Information Theory 60,
(2014) 643650.

K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang.
Affine images of isotropic measures,
Journal of Differential Geometry 99 (2015) 407442.

Y. Huang, E. Lutwak, D. Yang, G. Zhang.
Geometric measures in the dual BrunnMinkowski theory and their associated
Minkowski problems,
Acta Mathematica 216 (2016) 325388.
Publications
Unpublished articles
 D. Yang.
Gunther's
proof of Nash's isometric embedding theorem.
 J. Goodman and D. Yang. Local solvability of nonlinear partial differential equations of real principal type.
 C. T. Yang (as told to D. Yang). Memories of Chern
 C. T. Yang. Equivalence of the AlexanderKolmogorff and Čech Cohomology Theories. Dissertation, Tulane University, 1952.
Mathematical Fragments

DeTurck's trick for the prescribed Ricci equation

A simple proof of the Theorema Egregium of Gauss

Gromov's approach to solving underdetermined ODE's

Gunther's
proof of Nash's isometric embedding theorem.

Holonomy equals curvature.