# Gaoyong Zhang

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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 Ph.D. 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
the Busemann–Petty problem in <math>R^4</math>.^{[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]}

## Notable publications

- Zhang, Gaoyong (1991), "Restricted chord projection and affine inequalities",
*Geometriae Dedicata*,**39**: 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 R^4",
*Annals of Mathematics*,**149**: 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>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>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>L_p</math>-Minkowski problem",
*Transactions of the American Mathematical Society*,**356**(11): 4359–4370, doi:10.1090/S0002-9947-03-03403-2 - 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

- ↑ "Math Genealogy Gaoyong Zhang". Retrieved 12 September 2023.
- ↑ "Past Member of the Institute of Advanced Study". 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**: 213–222 - ↑ Zhang, Gaoyong (1999), "A positive solution to the Busemann-Petty problem in R4",
*Annals of Mathematics*,**149**: 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

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