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中山大学数学学院导师教师师资介绍简介-朱熹平

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简介:朱熹平, 中山大学数学学院教授。1989 年 2 月在中国科学院系统科学研究所获得理学博士学位; 1989 年 3 月起至今在中山大学任讲师、副教授、教授, 其中 2009-2013 被聘为中山大学逸仙****讲座教授。 1998 年度国家****科学基金获得者;分别于 2002 年和 2013 年被评为全国百篇优秀博士学位论文指导教师; 分别于 2004 年和 2016 年获 ICCM (国际华人数学家大会)的晨兴数学银奖和 ICCM 的陈省身奖;2013 年度教育部高等学校自然科学奖一等奖的第一完成人;2015 年度国家自然科学基金创新研究群体项目学术带头人;2016 年度国家自然科学奖二等奖项目“Ricci 流理论及其几何应用”的第一完成人。
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研究成果:主要从事几何分析领域的研究,为国际重大数学课题Thurston几何化猜测的最终证明做出了一份贡献。著名数学难题Poincaré猜测仅是Thurston?几何化猜测的小部分。1982-2002?年间,Hamilton?建立了利用?Ricci?流解决Thurston?几何化猜测的研究框架。2002-2003?年间,Perelman在互联网上贴出了三篇论文,简略地提出了完成?Hamilton?框架的论证。Hamilton-Perelman?理论能否给出?Thurston?几何化猜测的证明是当时国际数学界众所关心的问题。全世界至少有三个团队在自觉地研究此论证的正确性:曹怀东-朱熹平,Morgan-田刚,Kleiner-Lott。于?2006?年,朱熹平和曹怀东完成了所有细节并发表了Thurston?几何化猜测的完整证明。美国科学院院士、邵逸夫奖获得者?Hamilton?在?2006?年国际数学家大会的一小时演讲摘要中写道:“A full exposition has been written recently by H.-D. Cao and X.-P. Zhu”。美国《科学》杂志把Poincaré猜测的解决列为?2006?年度全球十大科研进展之一。
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他与陈兵龙、邓少雄合作给出了四维正迷向曲率流形的全面分类,并证明了四维情形的由Wolf?奖和?Abel?奖获得者Gromov所提出的基本群结构猜测(这也被?Schoen?在2010年国际数学家大会的一小时大会报告中重新提出);与陈兵龙合作解决了Ricci?流的唯一性公开问题;与顾会玲合作证明了Ricci流理论创始人(邵逸夫奖获得者)Hamilton提出的第二类奇点的猜测;与张会春合作证实了(美国艺术与科学院院士、B?cher奖获得者)林芳华的关于度量空间上调和映射的正则性猜测。
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Selected Publications of Xi-Ping Zhu
[1]. Lipschitz continuity of harmonic maps between Alexandrov spaces, with H.-C. Zhang, Invent. Math., 211 (2018), no. 3, 863-934.
[2]. On the local extension of the future null infinity, with J.-B. Li, J. Differential Geometry. 110 (2018), no.1,73-133.
[3]. Yau’s gradient estimates on Alexandrov spaces, with H.-C. Zhang, J. Differential Geometry, 91(2012), 445-522.
[4]. Complete classification of compact four-manifolds with positive isotropic curvature, with B.-L. Chen and S.-H. Tang, J. Differential Geometry, 91(2012), 41-80.
[5]. Ricci curvature on Alexandrov spaces and rigidity theorems, with H.-C. Zhang, Communications in Analysis and Geometry, Vol.18, No.3, (2010), 503-553.
[6]. Recent developments on Hamilton’s Ricci flow, with H.-D. Cao and B.-L. Chen, Survey in Differential Geometry, Volume 12, (2008), 47-112, International Press.
[7]. The existence of Type II singularities for the Ricci flow on Sn+1, with H.-L. Gu, Communications in Analysis and Geometry, Vol. 16, 3(2008), 467-494.
[8]. Ricci flow with surgery on four-manifolds with positive isotropic curvature, with B.-L. Chen, J. Differential Geometry, 74(2006), 177-264.
[9]. Uniqueness of the Ricci flow on complete noncompact manifolds, with B.-L. Chen, J. Differential Geometry, 74(2006), 119-154.
[10]. A complete proof of the Poincare and geometrization conjectures - application of the Hamilton-Perelman theory of the Ricci flow, with H.-D. Cao, Asian J. Math., Vol. 10, No. 2, pp 165-492, June 2006.
[11]. Sharp dimension estimates of holomorphic functions and rigidity, with B.-L. Chen, X.-Y. Fu and L. Yin, Transactions A. M. S., 358(2005), 1435-1454.
[12]. Volume growth and curvature decay of positively curved K¨ahler manifolds, with B.-L. Chen, Quarterly Journal of Pure and Applied Mathematics, Vol. 1, No. 1, pp 68-108, 2005.
[13]. A uniformization theorem for complete noncompact K¨ahler surface with positive bisectional curvature, with B.-L. Chen and S.-H. Tang, J. Differential Geometry, 67(2004), no.3, 519-570.
[14]. On complete noncompact K¨ahler manifolds with positive bisectional curvature, with B.-L. Chen, Math. Ann., 327(2003), 1-23.
[15]. Ricci flow on compact K¨ahler manifolds with positive bisectional curvature, with H.-D. Cao and B.-L. Chen, C. R. Acad. Sci. Paris, Ser. I, 337(2003), 781-784.
[16]. Lectures on mean curvature flow, Amer. Math. Soc. and International Press, (2002), 150 pages.
[17]. A gap theorem for complete noncompact manifolds with nonnegative Ricci curvature, with B.-L. Chen, Comm. Anal. Geom., 10, (2002), no.1, 217-239.
[18]. The curve shortening problem, with K.-S. Chou, Chapman and Hall/CRC, (2001), 255 pages.
[19]. Complete Riemannian manifolds with pointwise pinched curvature, with B.-L. Chen, Invent. Math., 140(2000), no.2, 423-452.
[20]. Anisotropic flows for convex plane curves, with K.-S. Chou, Duke Math. J., 97(1999), no.3, 579-619.
[21]. Shortening complete plane curves, with K.-S. Chou, J. Differential Geometry, 50(1998), no.3, 471-504.
[22]. Asymptotic behavior of anisotropic curve flows, J. Differential Geometry, 48(1998), no.2, 225-274.
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