Erwin Lutwak

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 became an Inaugural Fellow of the American Mathematical Society^[5] in 2012 and received an honorary doctorate of the TU Wien in 2014.^[6]

Work[]

Erwin Lutwak is known for his Dual Brunn Minkowski Theory,^[7] his notion of intersection body and his contribution to the solution of the Busemann–Petty problem,^[8] for proving the long-conjectured^[9] upper-semicontinuity of affine surface area,^[10] his contributions to the L_p Brunn Minkowski Theory and, in particular, his L_p Minkowski problem^[11] and its solution in important cases.^[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[]

• Erwin Lutwak. Dual mixed volumes. Pacific J. Math. 58 (1975), no. 2, 531–538.
• Erwin Lutwak. Intersection bodies and dual mixed volumes. Adv. Math. 71 (1988), no. 2, 232–261.
• Erwin Lutwak. Centroid bodies and dual mixed volumes. Proc. London Math. Soc. (3) 60 (1990), no. 2, 365–391.
• Erwin Lutwak. The Brunn-Minkowski-Firey theory. I. Mixed volumes and the Minkowski problem. J. Differential Geom. 38 (1993), no. 1, 131–150.
• Erwin Lutwak and Vladimir Oliker. On the regularity of solutions to a generalization of the Minkowski problem. J. Differential Geom. 41 (1995), no. 1, 227–246.
• Erwin Lutwak. The Brunn-Minkowski-Firey theory. II. Affine and geominimal surface areas. Adv. Math. 118 (1996), no. 2, 244–294.
• Erwin Lutwak and Gaoyong Zhang. Blaschke-Santaló inequalities. J. Differential Geom. 47 (1997), no. 1, 1–16.
• Erwin Lutwak, Deane Yang, and Gaoyong Zhang. L_p affine isoperimetric inequalities. J. Differential Geom. 56 (2000), no. 1, 111–132.
• Erwin Lutwak, Deane Yang, and Gaoyong Zhang. A new ellipsoid associated with convex bodies. Duke Math. J. 104 (2000), no. 3, 375–390.
• Erwin Lutwak, Deane Yang, and Gaoyong Zhang. Sharp affine L_p Sobolev inequalities. J. Differential Geom. 62 (2002), no. 1, 17–38.
• Erwin Lutwak, Deane Yang, and Gaoyong Zhang. On the L_p-Minkowski problem. Trans. Amer. Math. Soc. 356 (2004), no. 11, 4359–4370.
• Erwin Lutwak, Deane Yang, and Gaoyong Zhang. L_p John ellipsoids. Proc. London Math. Soc. (3) 90 (2005), no. 2, 497–520.
• Christoph Haberl, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. The even Orlicz Minkowski problem. Adv. Math. 224 (2010), no. 6, 2485–2510.
• Erwin Lutwak, Deane Yang, and Gaoyong Zhang. Orlicz centroid bodies. J. Differential Geom. 84 (2010), no. 2, 365–387.
• Erwin Lutwak, Deane Yang, and Gaoyong Zhang. Orlicz projection bodies. Adv. Math. 223 (2010), no. 1, 220–242.
• Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. The log-Brunn-Minkowski inequality. Adv. Math. 231 (2012), no. 3-4, 1974–1997.
• Károly J. Böröczky, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. The logarithmic Minkowski problem. J. Amer. Math. Soc. 26 (2013), no. 3, 831–852.
• Yong Huang, Erwin Lutwak, Deane Yang, and Gaoyong Zhang. Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems. Acta Math. 216 (2016), no. 2, 325–388.
• Károly J. Böröczky, Erwin Lutwak, Deane Yang, Gaoyong Zhang, and Yiming Zhao. The Gauss image problem. Comm. Pure Appl. Math. 73 (2020), no. 7, 1406–1452.

References[]

External links[]

• Erwin Lutwak publications indexed by Google Scholar