Deane   Yang

Deane Yang

Professor

Mathematics

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.

See my personal homepage

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

Awards + Distinctions

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

Research Interests

Convex geometric analysis, Riemannian geometry, Partial differential equations