l Deane Yang

Contact Info

email:
deane.yang@nyu.edu

Office: Rogers Hall 305A

Mailing address:
Six Metrotech Center
Brooklyn, New York 11201

Deane Yang, Professor of Mathematics

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.

Survey papers

Selected refereed journal articles

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  1. E. Lutwak, D. Yang, G. Zhang. A new ellipsoid associated with convex bodies, Duke Mathematical Journal 104 (2000) 375-390.
  2. E. Lutwak, D. Yang, G. Zhang. Lp affine isoperimetric inequalities, Journal of Differential Geometry 56 (2000) 111-132.
  3. E. Lutwak, D. Yang, G. Zhang. A new affine invariant for polytopes and Schneider's projection problem. Transactions of the AMS 353 (2001) 1767-1779.
  4. O. Guleryuz, E. Lutwak, D. Yang, G. Zhang. Information theoretic inequalities for contoured probability distributions, IEEE Transactions on Information Theory 48 (2002) 2377-2383.
  5. E. Lutwak, D. Yang, G. Zhang. The Cramer-Rao inequality for star bodies, Duke Mathematical Journal 112 (2002) 59-81.
  6. E. Lutwak, D. Yang, G. Zhang. Sharp affine Lp Sobolev Inequalities, Journal of Differential Geometry 62 (2002) 17-38.
  7. E. Lutwak, D. Yang, G. Zhang. Moment-entropy inequalities, Annals of Probability 32 (2004) 757-774.
  8. E. Lutwak, D. Yang, G. Zhang. On the Lp-Minkowski problem, Transactions of the AMS 356 (2004) 4359-4370.
  9. D. Hug, E. Lutwak, D. Yang, and G. Zhang, On the Lp Minkowski problem for polytopes, Discrete and Computational Geometry (2005) 699-715.
  10. E. Lutwak, D. Yang, and G. Zhang, Lp John ellipsoids, Proceedings of the London Mathematical Society 90 (2005) 497-520.
  11. E. Lutwak, D. Yang, and G. Zhang, Volume inequalities for subspaces of Lp, Journal of Differential Geometry 68 (2004) 159-184.
  12. W. Chen, R. Howard, E. Lutwak, D. Yang, and G. Zhang, A generalized affine isoperimetric inequality, Journal of Geometric Analysis 14 (2004) 597-612.
  13. E. Lutwak, D. Yang, G. Zhang. Cramer-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information, IEEE Transactions on Information Theory 51 (2005) 473-478.
  14. E. Lutwak, D. Yang, G. Zhang. Optimal Sobolev Norms and the Lp Minkowski Problem, International Mathematical Research Notices (2006) 1-21.
  15. E. Lutwak, D. Yang, G. Zhang. Volume Inequalities for Isotropic Measures, American Journal of Mathematics 129 (2007) 1711-1723.
  16. E. Lutwak, D. Yang, G. Zhang. Moment-entropy inequalities for a random vector, IEEE Transactions on Information Theory 53 (2007) 1603-1607.
  17. A. Cianchi, E. Lutwak, D. Yang, G. Zhang. Affine Moser-Trudinger and Morrey-Sobolev inequalities, Calculus of Variations and PDE's 36 (2009) 419-436.
  18. E. Lutwak, D. Yang, G. Zhang. Orlicz projection bodies, Advances in Mathematics 223 (2010) 220-242.
  19. C. Haberl, E. Lutwak, D. Yang, G. Zhang. The even Orlicz Minkowski problem, Advances in Mathematics 224 (2010) 2485-2510.
  20. E. Lutwak, D. Yang, G. Zhang. A volume inequality for polar bodies, Journal of Differential Geometry 84 (2010) 163-178.
  21. E. Lutwak, D. Yang, G. Zhang. Orlicz centroid bodies, Journal of Differential Geometry 84 (2010) 365-387.
  22. 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) 869-873.
  23. E. Lutwak, D. Yang, G. Zhang. The Brunn-Minkowski-Firey inequality for nonconvex sets, Advances in Applied Mathematics 48 (2012) 407-413.
  24. E. Lutwak, S. Lv, D. Yang, G. Zhang. Extensions of Fisher information and Stam's inequality, IEEE Transactions in Information Theory (2012) 1319-1327.
  25. K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang. The log-Brunn-Minkowski inequality, Advances in Mathematics 231 (2012) 1974-1997.
  26. K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang. The logarithmic Minkowski problem, Journal of the American Mathematics Society 26 (2013) 831-852.
  27. E. Lutwak, S Lv, D. Yang, G. Zhang. Affine moments of a random vector, IEEE Transactions in Information Theory 59 (2013) 5592-5599
  28. A. Cianchi, E. Lutwak, D. Yang, G. Zhang. A Unified Approach to Cramér-Rao Inequalities, IEEE Transactions in Information Theory 60, (2014) 643--650.
  29. K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang. Affine images of isotropic measures, Journal of Differential Geometry 99 (2015) 407--442.

Publications

Unpublished articles

  1. D. Yang. Gunther's proof of Nash's isometric embedding theorem.
  2. J. Goodman and D. Yang. Local solvability of nonlinear partial differential equations of real principal type.
  3. C. T. Yang (as told to D. Yang). Memories of Chern
  4. C. T. Yang. Equivalence of the Alexander-Kolmogorff and Čech Cohomology Theories. Dissertation, Tulane University, 1952.

Mathematical Fragments (brief notes about simple mathematical ideas)

Department of Mathematics