个人简介
1.教育背景
·博士(基础数学/微分几何),杭州大学，1994
·硕士(基础数学/微分几何),杭州大学，1991
·学士(数学)，徐州师范学院（今江苏师范大学）,1986
2.工作履历
·2004-至今，教授浙江大学数学系
·1998-2004，副教授浙江大学数学系
·1994-1998，副教授(1997-1998)，讲师(1994-1997)
杭州大学数学系
3.短期访问
·University of Kiel,Germany,Feb.-July,2000.
·University of Tuebingen,Germany,June,2000.
·The Australian National University,Australia,July-August,2001.
·中国科学院数学与系统科学研究院数学研究所，May-August,2002.
·The Australian National University,Australia,Sept.2002-Feb.2003.
·National University of Singarpore,June,2004.
·UCSD,USA,July,2005.
·The Australian National University,Australia,May-Aug.2006.
·MSRI,Berkeley,USA,Jan-Mar,2007.
·The Scuola Normale Superiore,Pisa,Italy,Jul.2009.
·The Australian National University,Australia,Jul.-Dec,2010.
·The Australian National University,Australia,Jan.-Jun,2016.
教学与课程
Year 2019-2020
Autumn-Winter:Geometry（求是班几何学）
Year 2018-2019
Spring:Riemannian Geometry-A Part of the PhD course:Modern Mathematics(Wed 6-8,4th floor)
Spring-Summer:Differential Geometry(微分几何)
Autumn-Winter:Geometry（求是班几何学）
Year 2017-2018
Spring:Riemannian Geometry-A Part of the PhD course:Modern Mathematics(Wed 6-8,4th floor)
Spring-Summer:Geometric Analysis(for graduate,Tuesday 6-8,Ouyang Blg 316)
Spring-Summer:Differential Geometry(微分几何)
Autumn-Winter:Geometry（求是班几何学）
Autumn-Winter:Nonlinear Analysis on Riemannian Manifolds-For Graduates(流形上的非线性分析-研究生课程)
Year 2016-2017
Spring:Riemannian Geometry-A Part of the PhD course:Modern Mathematics
Spring-Summer:Selected Topics on Modern Mathematics-Differential Geometry
(现代数学进展-微分几何选讲)
Spring-Summer:Differential Geometry(微分几何)
Autumn-Winter:Geometry（求是班几何学）
Autumn-Winter:Differential Manifolds(微分流形)
Year 2015-2016
Autumn-Winter:Geometry（求是班几何学）
Autumn-Winter:Riemannian Geometry-For Graduates(黎曼几何)
Year 2014-2015
Summer School course:Hyperbolic Geometry(Homework assignment)-By Prof.Yi Liu(7月21日周二交王枫博士)
Spring-Summer:Differential Geometry(微分几何)
Spring-Summer:Riemannian Geometry(黎曼几何)
Spring:Riemannian Geometry-A Part of the PhD course:Modern Mathematics
Autumn-Winter:Geometry（求是班几何学）
Autumn-Winter:Differential Manifolds(微分流形)(王枫博士主讲)(期中练习题)
Autumn-Winter:Nonlinear Analysis on Riemannian Manifolds-For Graduates(流形上的非线性分析-研究生课程)
Year 2013-2014
Spring-Summer:Differential Geometry(微分几何)
Spring-Summer:Riemannian Geometry(黎曼几何)
Spring:Riemannian Geometry-A Part of the PhD course:Modern Mathematics
Autumn-Winter:General Geometry（一般几何学）
Autumn-Winter:Differential Manifolds(微分流形)
Autumn-Winter:Riemannian Geometry-For Graduates(黎曼几何)
Year 2012-2013
Spring-Summer:Differential Geometry(微分几何)
Spring-Summer:Riemannian Geometry(黎曼几何)
Spring（March-April）:Riemannian Geometry-A Part of the PhD course:Modern Mathematics
Autumn-Winter:General Geometry（一般几何学）
Autumn-Winter:Differential Manifolds(微分流形)
科研
研究兴趣：
本人主要研究兴趣在于具有一定几何或物理背景的微分几何和偏微分方程，包括预定曲率问题，高阶Yamabe问题，以及曲率流问题。
曾经或正在承担的研究项目：
国家自然科学基金面上项目，批准号：＃11971424，名称：“几何流及其在凸几何、复几何以及数学广义相对论中的应用”，起止年月：2020/1—2023/12，项目负责人，该项目正在进行中；
国家自然科学基金面上项目，批准号：＃11571304，名称：“流形上的一类完全非线性偏微分方程”，起止年月：2016/1—2019/12，项目负责人，该项目正在进行中；
国家自然科学基金重点项目，批准号：＃11131007，名称：“流形上的几何与分析”，起止年月：2012/1—2016/12，项目参加人，该项目已经完成；
国家自然科学基金重点项目，批准号：＃10831008，名称：“流形上的典则结构及在几何拓扑中的应用”，起止年月：2009/1—2012/12，项目参加人，该项目已经完成；
国家自然科学基金面上项目，批准号：＃10771189，名称：“与曲率有关的若干几何分析问题”，起止年月：2008/1—2010/12，项目负责人，该项目已经完成；
国家自然科学基金面上项目，批准号：＃10471122，名称：“曲率流及其在微分几何中的应用”，起止年月：2005/1—2007/12，项目负责人，该项目已经完成；
浙江省自然科学基金面上项目，批准号：＃102033，名称：“曲率流在微分几何中的应用”，起止年月：03/1—05/12，项目负责人，该项目已经完成。
研究成果
1、高阶（完全非线性型）Yamabe问题的解的存在性。代表作：
The Yamabe problem for higher order curvatures.(with Trudinger and X.-J.Wang)J.Differential Geom.77(2007),no.3,515–553.
Admissible Metrics in theσ-k-Yamabe Equation,Proc.AMS,Vol 136(2008),no.5,1795-1802.
Local estimates for elliptic equations arising in conformal geometry，(with Yan He)International Mathematics Research Notices,2013,258-290,(2013).doi:10.1093/imrn/rnr262.
On existence of the prescribing k-curvature problem on manifolds with boundary.(with Yan He)Comm.Anal.Geom.19,no.1,53–77,(2011).
2、预定曲率问题。代表作：
Interior curvature bounds for a class of curvature equations.(with Urbas and X.-J.Wang)Duke Math.J.123(2004),no.2,235–264.
Convex hypersurface of prescribed Weingarten curvatures,(with Neil Trudinger and Xu-Jia Wang),Comm.in Analysis and Geometry,12(2004),213-232.
Closed Hypersurfaces with Prescribed Weingarten Curvature in Riemannian Manifolds,(with Qi-Rui Li)Calculus of Variations and Partial Differential Equations,DOI 10.1007/s00526-012-0540-1,2013.
Prescribed Weingarten Curvature Equations,(with Neil Trudinger and Xu-Jia Wang)Recent development in Geometry and Analysis,ALM 23,pp.359-386,2012.
3、平均曲率流和Ricci流。代表作：
Singularity Profile in the Mean Curvature Flow,(with Xu-Jia Wang)Methods and Applications of Analysis,16(2009),no.2,139-156.
Regularity and Singularity in the Mean Curvature Flow,(with Xu-Jia Wang)Trends in Partial Differential Equations,Higher Education Press and International Press,Beijing-Boston,2009,399-436.
Total mass under connection Ricci flow.(with Chao Wu)J.Geom.Phys.,61,no.10,1965–1975,(2011).doi:10.1016/j.geomphys.2011.05.006
Evolving hypersurfaces by their mean curvature in the background manifold evolving by Ricci flow.(with Haobin Yu)Commun.Contemp.Math.19(2017),no.1,1550092,27 pp.
Singularity of connection Ricci flow for three-manifolds.(with Haobin Yu)J.Math.Phys.58(2017),no.9,091503,20 pp.
4、其他的曲率流、曲率方程、CR几何流等。代表作：
Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems，(with Qi-Rui Li and Xu-Jia Wang)J.Euro.Math.Soc.(in press)
Convergence of the CR Yamabe Flow,(with Pak Tung Ho and Kun-Bo Wang)Mathematische Annalen(online 2017)
Enclosed convex hypersurfaces with maximal affine area,(with Neil Trudinger and Xu-Jia Wang),Math.Z.,252(2006),no.3,497-510.
Deforming metrics with negative curvature by a fully nonlinear flow,(with Jiayu Li),Calc.Var.PDE.,23(2005),no.1,33-50.
研究生
已经毕业博士生和工作单位：
2005-2010吴超，浙江工业大学
2008-2014李奇睿，澳大利亚国立大学-浙江大学
2008-2012袁丽霞，上海师范大学
2010-2015于浩斌，杭州师范大学
2012-2018王坤博，中国计量学院
2013-2018王礼胜，江西井冈山大学
2012-2019薄乐阳,北京大学
2015-2020易彩虹，杭州师范大学
已经毕业硕士生和工作单位：
2007-2009岳贇，支付宝公司
2007-2009郑佳林，武钢三中
2010-2012杨玉，华为公司（杭州）
2011-2013史鹏帅，美国东北大学-北京大学
2011-2013张鹏，美国
2013-2015王瑛，杭州学军中学
在读研究生：
博士生
2015-夏树灿（2015）
2015-王嘉项（2018转博）
2016-张怀宇（2018转博）
2019-刘馨莹（2019）
硕士生
2017-胡为
2019-薛珂
近期论文
查看导师新发文章
（温馨提示：请注意重名现象，建议点开原文通过作者单位确认）
The planar Lp dual Minkowski problem, (with Shucan Xia) Science China Mathematics, online http://engine.scichina.com/doi/10.1007/s11425-020-1682-9
Regularity of weak solutions to a class of complex Hessian equations on Ka ̈hler manifolds, (with Jiaxiang Wang) JOURNAL OF MATHEMATICAL STUDY, accepted.
An Anisotropic shrinking flow and L_p Minkowski problem, (with Caihong Yi) Comm. Analysis and Geometry, accepted. http://arxiv.org/abs/1905.04679
A class of anisotropic expanding curvature flows, (with Caihong Yi) DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS(DCDS-A), 40(2020), no. 4: 2017–2035. doi:10.3934/dcds.2020104.
Asymptotic Convergence for a Class of Fully Nonlinear Curvature Flows, (with Qi-Rui Li and Xu-Jia Wang) The Journal of Geometric Analysis 30 (2020), no. 1, 834–860.https://doi.org/10.1007/s12220-019-00169-4.
Prescribed k-curvature problems on complete noncompact Riemannian manifolds, (with Ji-Xiang Fu and Li-xia Yuan) International Mathematics Research Notices, rny262, https://doi.org/10.1093/imrn/rny262 (online)
Some Rigidity Properties for Manifolds with Constant k-Curvature of Modified Schouten Tensor, (with Leyang Bo) The Journal of Geometric Analysis 29(2019), no. 3, 2862-2887, http://link.springer.com/article/10.1007/s12220-018-0097-0
Critical metrics with cyclic parallel Ricci tensor for volume functional on manifolds with boundary, (with Lisheng Wang) Geometriae Dedicata, 201(2019), 243-251. http://link.springer.com/article/10.1007/s10711-018-0391-9
On a complex Hessian flow, (with Jiaxiang Wang) Pacific J Math, 300(2019), no. 1, 159-177. DOI: 10.2140/pjm.2019.300.159
Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems，(with Qi-Rui Li and Xu-Jia Wang) J. Euro. Math. Soc.22 (2020), no. 3, 893–923. https://www.ems-ph.org/journals/show_pdf.php?jrn=jems&doi=936
Convergence of the CR Yamabe Flow, (with Pak Tung Ho and Kun-Bo Wang) Mathematische Annalen, 373(2019), 1-2, 743-830. https://doi.org/10.1007/s00208-017-1634-z
The Exponential Convergence of the CR Yamabe Flow, (with Kunbo Wang) Science China Mathematics 63(2020), no. 5: 979-992. http://engine.scichina.com/doi/10.1007/s11425-017-9365-7
Bach-flat critical metrics for quadratic curvature functionals, (with Lisheng Wang) Ann Glob Anal Geom., 54(2018) 3, 365-375. https://doi.org/10.1007/s10455-018-9606-4
Variational properties of quadratic curvature functionals, (with Lisheng Wang) Science China Mathematics, 62(2019), no. 9, 1765-1778. https://doi.org/10.1007/s11425-017-9232-6
The k-Yamabe solitons and the quotient Yamabe solitons. (with Pak Tung Ho and Leyang Bo) Nonlinear Anal. 166 (2018), 181–195.
Singularity of connection Ricci flow for three-manifolds. (with Haobin Yu) J. Math. Phys. 58 (2017), no. 9, 091503, 20 pp.
Evolving hypersurfaces by their mean curvature in the background manifold evolving by Ricci flow.(with Haobin Yu) Commun. Contemp. Math. 19 (2017), no. 1, 1550092, 27 pp.
F-stability of f-minimal hypersurface. (with Haobin Yu) Proc. Amer. Math. Soc. 143 (2015), no. 8, 3619–3629.
A class of Neumann problems arising in conformal geometry. (with Li-xia Yuan) Pacific J. Math. 270 (2014), no. 1, 211–235.
Prescribing curvature problems on the Bakry-Emery Ricci tensor of a compact manifold with boundary. (with Li-Xia Yuan) Chin. Ann. Math. Ser. B 35 (2014), no. 1, 139–160.
Closed Hypersurfaces with Prescribed Weingarten Curvature in Riemannian Manifolds, (with Qi-Rui Li) Calculus of Variations and Partial Differential Equations, DOI 10.1007/s00526-012-0540-1, 2013.
Local estimates for elliptic equations arising in conformal geometry，(with Yan He) International Mathematics Research Notices, 2013, 258-290, (2013). doi:10.1093/imrn/rnr262.
The k-Yamabe flow on manifolds with boundary,(with Li-Xia Yuan) Nonlinear Analysis, 82, 127-141, (2013). http://dx.doi.org/10.1016/j.na.2013.01.008
The k-Yamabe problem, (with Neil Trudinger and Xu-Jia Wang) Surveys in Differential Geoemtry，Vol. 17, 427-457, 2012.
Prescribed Weingarten Curvature Equations, (with Neil Trudinger and Xu-Jia Wang) Recent development in Geometry and Analysis, ALM 23, pp.359-386, 2012.
On existence of the prescribing k-curvature problem on manifolds with boundary. (with Yan He) Comm. Anal. Geom. 19 , no. 1, 53–77, (2011).
Total mass under connection Ricci flow. (with Chao Wu) J. Geom. Phys., 61 , no. 10, 1965–1975, (2011). doi:10.1016/j.geomphys.2011.05.006
Some Dirichlet problems arising from conformal geometry,(with Qi-Rui Li) Pacific J. Math.,251，no.2, 337-359,（2011）.
Prescribing the symmetric function of the eigenvalues of the Schouten tensor, (with Yan He) Proc. Amer. Math. Soc., 139(3): 1127-1136, 2011.
Rotationally symmetric translating soliton of H^{k}-Flow, (with Chao Wu) Sciences in China-Series A (Mathematics), 53(4), 1011-1016, (2010).
Regularity and Singularity in the Mean Curvature Flow, (with Xu-Jia Wang) Trends in Partial Differential Equations, Higher Education Press and International Press, Beijing-Boston, 2009, 399-436.
Singularity Profile in the Mean Curvature Flow, (with Xu-Jia Wang) Methods and Applications of Analysis, 16 (2009), no. 2, 139-156.
On asymptotic behavior for singularities of the powers of mean curvature flow, (with Chao Wu) Chinese Annals of Mathematics - Series B, 30(2009), 51-66. DOI: 10.1007/s11401-007-0448-9
Admissible Metrics in the -Yamabe Equation, Proc. AMS, Vol 136 (2008), no. 5, 1795-1802.
The Yamabe problem for higher order curvatures, (with Neil Trudinger and Xu-Jia Wang), JDG, Vol. 77(2007), no. 3, 515-553.
A class of fully nonlinear equations arising from conformal geometry, (with Yan Zhang), Math. Z., Vol. 255, (2007), No. 1, 17-34.
Enclosed convex hypersurfaces with maximal affine area, (with Neil Trudinger and Xu-Jia Wang), Math. Z., 252(2006), no. 3, 497-510.
Deforming metrics with negative curvature by a fully nonlinear flow,(with Jiayu Li), Calc.Var.PDE., 23(2005), no.1, 33-50.
Interior curvature bounds for a class of curvature equations,(with J. Urbas and Xu-Jia Wang), Duke Math. J., 123(2004), no.2, 235-264.
Convex hypersurface of prescribed Weingarten curvatures,(with Neil Trudinger and Xu-Jia Wang), Comm. in Analysis and Geometry, 12(2004), 213-232.
On the affine diameter of closed convex hypersurfaces, (with Neil S. Trudinger), Bull. Australian Math. Soc., 68(2003), 431-437.
Geometry of complete hypersurfaces evolved by mean curvature flow, Chin. Ann. of Math., 24(B)(2003), 123-132.
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