Gaoyong Zhang

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 $R^{4}$ .^[7] He is known for his contributions (in collaboration with Erwin Lutwak and Deane Yang) to the L_p 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, S2CID 123311639
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 $\mathbb {R} ^{4}$ ", Annals of Mathematics, 149 (2): 535–543, doi:10.2307/120974, JSTOR 120974, S2CID 14663005
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), " $L_{p}$ 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 $L_{p}$ Sobolev inequalities", Journal of Differential Geometry, 62 (1): 17–38, doi:10.4310/jdg/1090425527, S2CID 51769607
Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong (2004), "On the $L_{p}$ -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), " $L_{p}$ 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" (PDF), 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" (PDF), 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" (PDF), 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" (PDF), Communications on Pure and Applied Mathematics, 73 (7): 1406–1452, doi:10.1002/cpa.21898, S2CID 218957398
Lutwak, Erwin; Xi, Dongmeng; Yang, Deane; Zhang, Gaoyong (2024), "Chord measures in integral geometry and their Minkowski problems", Communications on Pure and Applied Mathematics, 77 (7): 3277–3330, doi:10.1002/cpa.22190

References

^ "Math Genealogy Gaoyong Zhang". Retrieved 12 September 2023.
^ "Past Member of the Institute of Advanced Study". 9 December 2019. Retrieved 12 September 2023.
^ "List of Fellows of the American Mathematical Society". Ams.org. Retrieved 12 September 2023.
^ "Advanced Nonlinear Studies – Editorial Board". Retrieved 2023-09-12.
^ "Proceedings of the American Mathematical Society – Editorial Board". Retrieved 2023-09-12.
^ Zhang, Gaoyong (1991), "Restricted chord projection and affine inequalities", Geometriae Dedicata, 39 (2): 213–222, doi:10.1007/BF00182294, S2CID 123311639
^ Zhang, Gaoyong (1999), "A positive solution to the Busemann-Petty problem in $\mathbb {R} ^{4}$ ", Annals of Mathematics, 149 (2): 535–543, doi:10.2307/120974, JSTOR 120974, S2CID 14663005.
^ Böröczky, Károly J.; 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.

External links

Gaoyong Zhang publications indexed by Google Scholar

[1] "Math Genealogy Gaoyong Zhang". Retrieved 12 September 2023.

[2] "Past Member of the Institute of Advanced Study". 9 December 2019. Retrieved 12 September 2023.

[3] "List of Fellows of the American Mathematical Society". Ams.org. Retrieved 12 September 2023.

[4] "Advanced Nonlinear Studies – Editorial Board". Retrieved 2023-09-12.

[5] "Proceedings of the American Mathematical Society – Editorial Board". Retrieved 2023-09-12.

[6] Zhang, Gaoyong (1991), "Restricted chord projection and affine inequalities", Geometriae Dedicata, 39 (2): 213–222, doi:10.1007/BF00182294, S2CID 123311639

[7] Zhang, Gaoyong (1999), "A positive solution to the Busemann-Petty problem in $\mathbb {R} ^{4}$ ", Annals of Mathematics, 149 (2): 535–543, doi:10.2307/120974, JSTOR 120974, S2CID 14663005.

[8] Böröczky, Károly J.; 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.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]