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朱小华
北京大学数学学院

朱小华，男，北京大学数学学院教授。

人物履历

教育经历

1990 杭州大学（现浙江大学） 学士

1995 杭州大学（现浙江大学） 博士

工作经历

  • 2001- 北京大学数学科学学院 教授
  • 2016.01- 2016.05 University of California at Berkely, MSRI, USA, Visiting Professor(Eisenberg Porfessor)
  • 2011.01-2011.05 Stony-Brook University, USA, Visiting Professor(Simon Professor)
  • 2006.01-2006.05 Wisconsin University-Madison, USA, Visiting Professor
  • 2002-2004 澳大利亚国立大学数学中心 研究员
  • 1999-2001 北京大学数学科学学院 副教授
  • 1997-1999 北京大学数学科学学院 博士后
  • 1997-1999 浙江大学数学科学学院 博士后

学术成果

  • Publications (in mathematics)
  • 1) K-energy on polarized compactifications of Lie groups, J. Func. Analysis, 275 (2018), 1023-1072. 2018.
  • 2) Structure of spaces with Bakry-Émery Ricci curvature bounded below, J. Reine Angew. Math (Crelle’s Journal), 2018, (with Wang, Feng).
  • 3) 3d steady Gradient Ricci Solitons with linear curvature decay, International Mathematics Research Notices, OI: 10.1093/imrn/rnx155, 2017.
  • 4) Asymptotic behavior of positively curved steady Ricci solitons. Trans. Amer. Math. Soc. 370 (2018), no. 4, 2855–2877, (with Deng, Yuxing).
  • 5) Bergman Kernels for a sequence of almost K\"{a}hler-Ricci solitons， Ann Fourier Institute, 67 (2017), no. 3, 1279–1320, (with Jiang, Wenshuai，Wang, Feng).
  • 6) Modified Futaki invariant and equivariant Riemann-Roch formula, Adv. Math., 286 (2016), 1205–1235. (with Wang, Feng, Zhou Bin)
  • 7) Fano manifolds with weak almost K\"ahler-Ricci solitons, Inter. Math. Res. Notices, 9 (2015), 2437–2464 ( with Wang, Feng ).
  • 8) Complete non-compact gradient Ricci solitons with nonnegative Ricci curvature, Math Zeit, 2015 ( with Deng, Yuxing ).
  • 9) Perelman's entropy and K\"ahler-Ricci flow on a Fano manifold. Trans. Amer. Math. Soc. 365 (2013), no. 12, 6669-6695( with Tian, Gang; Zhang, Shijin; Zhang, Zhenlei).
  • 10) Stability of K\"ahler-Ricci flow on a Fano manifold. Math. Ann. 356 (2013), no. 4, 1425-1454.
  • 11) Convergence of the K\"ahler-Ricci flow on Fano manifolds. J. Reine Angew. Math. 678 (2013), 223-245 ( with Tian, Gang).
  • 12) K\"ahler-Ricci solitons on toricFanoorbifolds. Math. Z. 271 (2012), 1241-1251 ( with Shi, Y. L) .
  • 13) K\"ahler-Ricci flow on a toric manifold with positive first Chern class. Differential geometry, 323–336, Adv. Lect. Math. (ALM), 22, Int. Press, Somerville, MA, 2012.
  • 14) A global mean value inequality for plurisubharmonic functions on a compact K\"ahler manifold. Recent developments in geometry and analysis, 495-507, Adv. Lect. Math. (ALM), 23, Int. Press, Somerville, MA, 2012.
  • 15) An example of a singular metric arising from the blow-up limit in the continuity approach to K\"ahler-Einstein metrics. Pacific J. Math. 250 (2011), no. 1, 191-203 ( with Shi, Y. L).
  • 16) A form of Alexandrov-Fenchel inequality. Pure Appl. Math. Q. 6 (2010), no. 4, Special Issue: In honor of Joseph J. Kohn. Part 2, 999-1012 ( with Guan, Pengfei; Ma, Xi-Nan; Trudinger, Neil).
  • 17) Canonical metrics on toric manifolds. Trends in partial differential equations, 497-522, Adv. Lect. Math. (ALM), 10, Int. Press, Somerville, MA, 2010.
  • 18) Relative K-stability and modified K-energy on toric manifolds. Adv. Math. 219 (2008), no. 4, 1327-1362 ( with Zhou, Bin ) .
  • 19) K-stability on toric manifolds. Proc. Amer. Math. Soc. 136 (2008), no. 9, 3301-3307 ( with Zhou, Bin ).
  • 20) Minimizing weak solutions for Calabi'sextremal metrics on toric manifolds. Calc. Var. Partial Differential Equations 32 (2008), no. 2, 191-217 ( with Zhou, Bin ).
  • 21) Convergence of K\"ahler-Ricci flow. J. Amer. Math. Soc. 20 (2007), no. 3, 675-699 ( with Tian, Gang).
  • 22) K\"ahler-Ricci solitons on compact complex manifolds with $C_1 (M)>0$, Geom. Funct. Anal. (2005), no. 3, 697-719 ( with Cao, Huai-Dong; Tian, Gang ).
  • 23) K\"ahler-Ricci solitons on toric manifolds with positive first Chern class. Adv. Math. 188 (2004), no. 1, 87-103 (with Wang, X.J. ) .
  • 24) A new holomorphic invariant and uniqueness of K\"ahler-Ricci solitons. Comment. Math. Helv. 77 (2002), no. 2, 297-325 (with Tian, Gang).
  • 25) Explicit construction of extremalHermitian metrics with finite conical singularities on S_2,
  • Comm. Anal. Geom. 10 (2002), no. 1, 177-216 (with Lin, Chang Shou) .
  • 26) K\"ahler-Ricci soliton typed equations on compact complex manifolds with $C_1(M)>0$, J. Geom. Anal. 10 (2000), no. 4, 759-774.
  • 27) Extremal Hermitian metrics on Riemann surfaces with singularities. Duke Math. J. 104 (2000), no. 2, 181-210 ( with Wang, Guofang ) .
  • 28) Uniqueness of K\"ahler-Ricci solitons. Acta Math. 184 (2000), no. 2, 271-305 ( with Tian, Gang).
  • 29) A nonlinear inequality of Moser-Trudinger type. Calc. Var. Partial Differential Equations 10 (2000), no. 4, 349-354 ( with Tian, Gang).
  • 30) Uniqueness of K\"ahler-Ricci solitons on compact Kähler manifolds. C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 11, 991-995 ( with Tian, Gang).
  • 31) On stable complete minimal hypersurfaces in $R^{n+1}$, Amer. J. Math. 120 (1998), no. 1, 103-116 ( with Shen, Yi-Bing ).
  • Preprints:
  • 1) Singular limits of Kähler-Ricc flow on Fano $G$-manifolds, (with Yan Li, Gang Tian), arXiv:1807.09167
  • 2) The Fu-Yau equation on compact astheno-Kähler manifolds, (with Jianchun Chu, Liding Huang), arXiv:1803.01475
  • 3) The Fu-Yau equation in higher dimensions, (with Jianchun Chu, Liding Huang), arXiv: 1801.09351
  • 4) $G$-Sasaki manifolds and K-energy, (with Yan Li, Xiaohua Zhu), arXiv:1712.07934
  • 5) Higher dimensional steady Ricci solitons with linear curvature decay, (with Yuxing Deng), arXiv:1710.07815
  • 6) The $2$-nd Hessian type equation on almost Hermitian manifolds, (with Jianchun Chu, Liding Huang), arXiv:1707.04072
  • 7) Asymptotic behavior of positively curved steady Ricci Solitons, II, (with Yuxing Deng)
  • arXiv:1604.00142
  • 8) Steady Ricci solitons with horizontally $ε$-pinched Ricci curvature, (with Yuxing Deng), arXiv:1601.02111
  • 9) Perelman's W-functional and stability of Kähler-Ricci flow, (with Gang Tian), arXiv:0801.3504

科研项目

2014-2018 Singular theories in Kaehler geometry(国家自然科学基金)，230万

2013-2016 Cannonical metrics and Ricci flow(国家自然科学基金)，56万

2005-2009 国家杰出青年自然科学基金，102万

1998年5月 博士后基金

荣誉获奖

1) A winner of Prize of Qiu Shi Science and Technologies Foundation, 2001, HongKong

2) A winner of Chinese National Science Foundation for the Outstanding Young Scientists, 2004,

3) A winner of 2005 ICTP Prize in honour of Armand Borel, Italy

4) A winner of national science and technology prize, 2013, China

5) A winner of Prize of Chern S. S from Chinese Math. Society,2017[1]

参考资料

  1. ↑ 北京大学数学学院
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