Education
Harvard University, Class of 1983
Doctor of Philosophy, Mathematics
University of Pennsylvania, Class of 1979
Bachelor of Arts, Mathematics and Physics
Experience
Polytechnic University
Professor
From: September 1991 to present
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
Courses Taught
Calculus, differential geometry, analysis
Research Interests
Convex geometric analysis, Riemannian geometry, Partial differential equations
Awards + Distinctions
- Sloan Foundation Fellow, 1998-1990
- Inaugural AMS Fellow, 2012
Event Participation
Member, American Mathematical Society
Journal Articles
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.Favorite Books + Authors
Aside from textbooks, what other reading material would you recommend to your students?
Anything written by Richard Feynman
Please provide a brief description of your teaching philosophy
Help students learn how to learn mathematics
What do you enjoy most about teaching at Poly?
Helping students discover that they can do the math on their own without my help
Favorite Activities
Traveling and eating
Favorite quote:
"There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else -- but persistent.”
― Raoul Bott