Biography:Gaoyong Zhang
Gaoyong Zhang | |
|---|---|
| Nationality | American |
| Alma mater | Temple University |
| Known for | Convex geometry |
| Scientific career | |
| Fields | Mathematician |
| Institutions | Courant Institute of Mathematical Sciences |
Gaoyong Zhang is an American mathematician. He is professor 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
Gaoyong Zhang graduated from Temple University in Philadelphia with a PhD in 1995. His advisor was Eric Grinberg.[1] Before he became a professor at the Courant Institute at NYU, he was a member of the Institute of Advanced Study.[2]
Zhang became an Inaugural Fellow of the American Mathematical Society[3] in 2012. He is a member of the editorial board at Advanced Nonlinear Studies (De Gruyter)[4] and at the Proceedings of the American Mathematical Society.[5]
Work
Gaoyong Zhang is known for his inverse of the Petty projection inequality,[6] one of the few inequalities in convex geometry where simplices were proved to be extremals. He obtained a positive solution for the Busemann–Petty problem in [math]\displaystyle{ R^4 }[/math].[7] He is known for his contributions (in collaboration with Erwin Lutwak and Deane Yang) to the Lp Brunn Minkowski Theory and, in particular, his solution to the logarithmic Minkowski problem.[8]
Selected publications
- Zhang, Gaoyong (1991), "Restricted chord projection and affine inequalities", Geometriae Dedicata 39 (2): 213–222, doi:10.1007/BF00182294
- Lutwak, Erwin; Zhang, Gaoyong (1997), "Blaschke-Santaló inequalities", Journal of Differential Geometry 47 (1): 1–16, doi:10.4310/jdg/1214460036
- Zhang, Gaoyong (1999), "A positive solution to the Busemann-Petty problem in [math]\displaystyle{ \mathbb{R}^4 }[/math]", Annals of Mathematics 149 (2): 535–543, doi:10.2307/120974
- Zhang, Gaoyong (1999), "The affine Sobolev inequality", Journal of Differential Geometry 53: 183–202, doi:10.4310/jdg/1214425451
- Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2000), "[math]\displaystyle{ L_p }[/math] 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 [math]\displaystyle{ L_p }[/math] Sobolev inequalities", Journal of Differential Geometry 62 (1): 17–38, doi:10.4310/jdg/1090425527
- Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2004), "On the [math]\displaystyle{ L_p }[/math]-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), "[math]\displaystyle{ L_p }[/math] John ellipsoids", Proceedings of the London Mathematical Society, Series 3 90 (2): 497–520, doi:10.1112/S0024611504014996
- 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, https://projecteuclid.org/journals/acta-mathematica/volume-216/issue-2/Geometric-measures-in-the-dual-BrunnMinkowski-theory-and-their-associated/10.1007/s11511-016-0140-6.pdf
- 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
- ↑ "Math Genealogy Gaoyong Zhang". https://mathgenealogy.org/id.php?id=40006. Retrieved 12 September 2023.
- ↑ "Past Member of the Institute of Advanced Study". 9 December 2019. https://www.ias.edu/scholars/gaoyong-zhang. Retrieved 12 September 2023.
- ↑ "List of Fellows of the American Mathematical Society". http://www.ams.org/profession/fellows-list. Retrieved 12 September 2023.
- ↑ "Advanced Nonlinear Studies – Editorial Board". https://www.degruyter.com/journal/key/ans/html#editorial. Retrieved 2023-09-12.
- ↑ "Proceedings of the American Mathematical Society – Editorial Board". https://www.ams.org/publications/journals/journalsframework/procedit. Retrieved 2023-09-12.
- ↑ Zhang, Gaoyong (1991), "Restricted chord projection and affine inequalities", Geometriae Dedicata 39 (2): 213–222, doi:10.1007/BF00182294
- ↑ Zhang, Gaoyong (1999), "A positive solution to the Busemann-Petty problem in [math]\displaystyle{ \mathbb{R}^4 }[/math]", Annals of Mathematics 149 (2): 535–543, doi:10.2307/120974.
- ↑ 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.
External links
- Gaoyong Zhang publications indexed by Google Scholar
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