Erwin Lutwak (born 9 February 1946, Chernivtsi, now Ukraine), is a mathematician. Lutwak is professor emeritus at the Courant Institute of Mathematical Sciences at New York University in New York City. His main research interests are convex geometry and its connections with analysis and information theory.
Biography
He spent the earliest years of his childhood in the Soviet Union, Romania, Israel, Italy, and Venezuela before he settled in Brooklyn when he was ten. He graduated from the Polytechnic Institute of Brooklyn, now New York University Tandon School of Engineering with a B.S. in 1968, a M.S. in 1972 and with a Ph.D. in 1974. Before he became professor at the Courant Institute at NYU, he was a professor at New York University Tandon School of Engineering. His first position in 1975 was at the Polytechnic Institute of New York (which was created as a result of the merger of the Polytechnic Institute of Brooklyn and the NYU School of Engineering).[1]
He is a member of the editorial boards of the Advances in Mathematics,[2] the Canadian Journal of Mathematics,[3] the Canadian Mathematical Bulletin,[3] and the Cambridge University Press Encyclopedia of Mathematics and its Applications.[4] He is an Honorary Editor at Advanced Nonlinear Studies (De Gruyter).[5]
Work
Erwin Lutwak is known for his Dual Brunn Minkowski Theory,[6] his notion of intersection body and his contribution to the solution of the Busemann–Petty problem,[7] for proving the long-conjectured upper-semicontinuity of affine surface area,[8] his contributions to the Lp Brunn Minkowski Theory and, in particular, his Lp Minkowski problem[9] and its solution in important cases.[10]
Honors
Lutwak became an Inaugural Fellow of the American Mathematical Society[11] in 2012.
He received an honorary doctorate of the TU Wien in 2014.[12]
Personal life
Dr. Lutwak is married to Nancy Lutwak, M.D.. They have one daughter, Hope Lutwak, who graduated with a Bachelor of Science in 2018 from the Massachusetts Institute of Technology. The family resides in Manhattan.
Notable publications
Lutwak, Erwin (1975), "Dual mixed volumes", Pacific Journal of Mathematics, 58 (2): 531–538, doi:10.2140/pjm.1975.58.531
Lutwak, Erwin (1988), "Intersection bodies and dual mixed volumes", Advances in Mathematics, 71 (2): 232–261, doi:10.1016/0001-8708(88)90077-1
Lutwak, Erwin (1990), "Centroid bodies and dual mixed volumes", Proceedings of the London Mathematical Society, Series 3, 60 (2): 365–391, doi:10.1112/plms/s3-60.2.365
Lutwak, Erwin (1993), "The Brunn-Minkowski-Firey theory I: Mixed volumes and the Minkowski problem", Journal of Differential Geometry, 38 (1): 131–150, doi:10.4310/jdg/1214454097
Lutwak, Erwin; Oliker, Vladimir (1995), "On the regularity of solutions to a generalization of the Minkowski problem", Journal of Differential Geometry, 41 (1): 227–246, doi:10.4310/jdg/1214456011
Lutwak, Erwin (1996), "The Brunn-Minkowski-Firey theory II: Affine and geominimal surface areas", Advances in Mathematics, 118 (2): 244–294, doi:10.1006/aima.1996.0022
Lutwak, Erwin; Zhang, Gaoyong (1997), "Blaschke-Santaló inequalities", Journal of Differential Geometry, 47 (1): 1–16, doi:10.4310/jdg/1214460036
Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2000), " L p L_{p} affine isoperimetric inequalities", Journal of Differential Geometry, 56 (1): 111–132, doi:10.4310/jdg/1090347527
Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2000), "A new ellipsoid associated with convex bodies", Duke Mathematical Journal, 104 (3): 375–390, doi:10.1215/S0012-7094-00-10432-2
Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2002), "Sharp affine L p L_{p} Sobolev inequalities", Journal of Differential Geometry, 62 (1): 17–38, doi:10.4310/jdg/1090425527
Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2004), "On the L p L_{p}-Minkowski problem", Transactions of the American Mathematical Society, 356 (11): 4359–4370, doi:10.1090/S0002-9947-03-03403-2
Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2005), " L p L_{p} John ellipsoids", Proceedings of the London Mathematical Society, Series 3, 90 (2): 497–520, doi:10.1112/S0024611504014996, S2CID 121641085
Haberl, Christoph; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2010), "The even Orlicz Minkowski problem", Advances in Mathematics, 224 (6): 2485–2510, doi:10.1016/j.aim.2010.02.006
Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2010), "Orlicz centroid bodies", Journal of Differential Geometry, 84 (2): 365–387, doi:10.4310/jdg/1274707317
Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2010), "Orlicz projection bodies", Advances in Mathematics, 223 (1): 220–242, doi:10.1016/j.aim.2009.08.002
Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2012), "The log-Brunn—Minkowski inequality", Advances in Mathematics, 231 (3–4): 1974–1997, doi:10.1016/j.aim.2012.07.015
Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2013), "The logarithmic Minkowski problem", Journal of the American Mathematical Society, 26 (3): 831–852, doi:10.1090/S0894-0347-2012-00741-3
Huang, Yong; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2016), "Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems", Acta Mathematica, 216 (2): 325–388, doi:10.1007/s11511-016-0140-6
Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong; Zhao, Yiming (2020), "The Gauss image problem", Communications on Pure and Applied Mathematics, 73 (7): 1406–1452, doi:10.1002/cpa.21898
References
"Professor of Mathematics Erwin Lutwak Might Be Feted in the World's Capitals but Brooklyn Remains Home". Engineering.nyu.edu. Retrieved 26 November 2017.
"Advances in Mathematics - Editorial Board". Retrieved 15 January 2019.
"CJM/CMB Editorial Board". Retrieved 15 January 2019.
"Encyclopedia of Mathematics and its Applications". Retrieved 15 January 2019.
"Advanced Nonlinear Studies - Editorial Board". Retrieved 2023-09-12.
Lutwak, Erwin (1975), "Dual mixed volumes", Pacific Journal of Mathematics, 58 (2): 531–538, doi:10.2140/pjm.1975.58.531
Lutwak, Erwin (1988), "Intersection bodies and dual mixed volumes", Advances in Mathematics, 71 (2): 232–261, doi:10.1016/0001-8708(88)90077-1.
Lutwak, Erwin (1991), "Extended affine surface area", Advances in Mathematics, 85 (1): 39–68, doi:10.1016/0001-8708(91)90049-D.
Lutwak, Erwin (1993), "The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem.", Journal of Differential Geometry, 38: 131–150, doi:10.4310/jdg/1214454097.
Böröczky, Karoly; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2013), "The logarithmic Minkowski problem." (PDF), Journal of the American Mathematical Society, 26 (3): 831–852, doi:10.1090/S0894-0347-2012-00741-3.
"American Mathematical Society". Ams.org. Retrieved 26 November 2017.
"Technische Universität Wien : Akademische Würdenträger_innen". Tuwien.ac.at. Archived from the original on 21 February 2016. Retrieved 26 November 2017.
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