个人简介
2001年-今，浙江大学数学系教授。
教学与课程
2018春夏学期：《实变函数论》
研究成果
研究兴趣是多复变函数论。它研究多个复变量的全纯函数。这类函数与一个复变量的全纯函数完全不同：奇点不是孤立的(Hartogs现象),Cauchy-Riemann方程组只有在满足相容性条件下才可解,其位势论是非线性的，而一维时位势论是线性的(the complex Monge-Ampere operator vs.Laplacian operator),等等。最近我致力于发展多个四元变量的函数论，以及更一般的不同几何结构上的函数论。当交换的复数域被非交换的四元可除代数代替时，出现了许多新的现象。
更一般地，我对高维空间上的分析，有时候是其背后的代数结构感兴趣。在当代数学中经常一个低维的理论非常成功，而相应的高维理论却如此复杂，以至于人们知道得很少从而成为一种挑战。例如，扭结vs.高维扭结,4维Yang-Mills理论vs.维数>4,曲线的函数域vs.曲面的函数域,向量丛vs.(higher)gerbes,层vs.(higher)stacks,范畴vs.高维范畴(高维代数),可积性往往存在于2维,物理中有许多低维的可解模型而高维的情况我们知道很少,等等。
其他
Links:
http://www.math.zju.edu.cn
近期论文
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1.A discrete transformation and Triebel-Lizorkin spaces on the bidisc,Transactions of the American mathematical society 347:(4)(1995),1351-1364.
2.Estimates of the Einstein-Kahler metric on a weakly pseudoconvex domain in C^2,Mathematische Zeitschrift 223(1996),535-545.
3.Estimates for d-bar equation on the generalized complex ellipsoids,Science in China(Series A)44:(4),(2000),452-466.
4.Positive solution of a subelliptic nonlinear equation on the Heisenberg group,Canadian Mathematical Bulletin 44:(3)(2001),346-354
5.Holder regularity for d-bar on convex domains of finite strict type,Pacific Journal of Mathematics 198(2001),235-256.
6.Regularity of complex on nondegenerate Cauchy-Riemann manifolds,Science in China(Series A)44:(4)(2001),452-466.
7.Canonical contact forms on spherical CR manifolds，Journal of the European Mathematical Society,Vol.5,(2003),245-273。
8.Embeddability of some three-dimensional weakly pseudoconvex CR structures.Canad.Math.Bull.47(2004),no.1,133--143.
9.(With P.Greiner and W.Staubach)Relative index on small deformations of embeddable CR structures of finite type,Math.Nachr.278(2005),no.4,379--400.
10.Representations of SU(p,q)and CR geometry.I,J.Math.Kyoto Univ.45(2005),no.4,759--780.
11.The Teichmüller distance on the space of spherical CR structures.Sci.China Ser.A 49(2006),no.11,1523--1538.
12.N-capacity,N-harmonic radius and N-harmonic transplantation.J.Math.Anal.Appl.327(2007),no.1,155--174.
13.The Yamabe problem on quaternionic contact manifolds.Ann.Mat.Pura Appl.(4)186(2007),no.2,359--380.
14.On stability of CR-mappings between nilpotent lie groups of step two,Siberian Mathematical Journal,48,(2007),no.3,408-427.
15.On a conformally invariant variational problem on differential forms,Nonlinear Analysis,68(2008),828-844.
16.On non-homogeneous Cauchy-Fueter equations and Hartogs'phenomenon in several quaternionic variables,J.Geom.Phys.58,(2008),1203-1210.
17.Korn's inequality and Donati's theorem for the conformal Killing operator on pseudo-Euclidean space,J.Math.Anal.Appl.345,(2008),777-782.
18.(With Wu,Qingyan)Conformal mappings and CR mappings on the Engel group,Sci.China Ser.A 52(2009),no.12,2759-2773.
19.The k-Cauchy-Fueter complexes,Penrose transformation and Hartogs'phenomenon for quaternionic k-regular functions,J.Geom.Phys.60,(2010),513-530.
20.On the optimal control method in quaternionic analysis,Bull.Sci.Math.135(2011),no.8,988-1010.
21.The tangential Cauchy-Fueter complex on the quaternionic Heisenberg group,J.Geom.Phys.61,(2011),363-380.
22.(With Wu,Qingyan)The Beltrami equations for quasiconformal mappings on strictly pseudoconvex hypersurfaces,Sib.Math.J.53(2012),no.2,316-334
23.(With Kang,Qianqian)On Radon-Penrose transformation and k-Cauchy-Fueter operator,Sci.China Math.55(2012),no.9,1921-1936.
24.(With Kang,Qianqian)On Penrose integral formula and series expansion of k-regular functions on the quaternionic space H^n,J.Geom.Phys.64(2013),192-208.
25.On twistor transformations and invariant differential operator of simple Lie group G_{2(2)},J.Math.Phys.54(2013),013502.
26.(With Wan,Dongrui)Lelong-Jensen type formula,k-Hessian boundary measure and Lelong number for k-convex functions,J.Math.Pures Appl.(9)99(2013),no.6,635-654.
27.(With Der-Chen Chang and Irina Markina)On the Cauchy-Szego Kernel for Quaternion Siegel Upper Half-Space,Complex Anal.Oper.Theory 7(2013),no.5,1623-1654.
28.On the tangential Cauchy-Fueter operators on nondegenerate quadratic hypersurfaces in H^2,Math.Nachr.,286(2013),no.13,1353-1376.
29.(With Haimeng Wang)On octonionic regular functions and Szego projection on the Octonionic Heisenberg group,Complex Anal.Oper.Theory 8(2014),no.6,1285-1324.
30.On 3-gauge transformations,3-curvatures,and Gray-categories,J.Math.Phys.55(2014),043506.
31.(with F.F.Wu)The Bochner-type formula and the
rst eigenvalue of the sub-Laplacian on a contact Riemannian manifold,Differential Geometry and its application 37(2014),66-88.
32.On the 3-representations of groups and the 2-categorical traces,Theory and Applications of Categories 30(2015),No.56,1999-2047.
33.(With Dongrui Wan)Complex Hessian operator and Lelong number for unbounded m-subharmonic functions,Potential Anal.44(2016),no.1,53-69.
34.(With Der-Chen Chang and Irina Markina)On the Hodge-type decomposition and cohomology groups of k-Cauchy-Fueter complexes over domains in the quaternionic space,J.Geom.Phys.107(2016),15-34.
35.(With Dongrui Wan)Viscosity solutions to quaternionic Monge-Amp_x005fere equations,Nonlinear Anal.140(2016),69-81.
36.(With Yun Shi)On conformal qc geometry,spherical qc manifolds and convex cocompact subgroups of Sp(n+1,1),Ann.Global Anal.Geom.49(2016),no.3,271-307.
37.On the weighted L^2-estimate for the k-Cauchy-Fueter operator and the weighted k-Bergman kernel,J.Math.Anal.Appl.452(2017),no.1,685-707.
38.(With Yun Shi)The Szego kernel for k-CF functions on the quaternionic Heisenberg group,Appl.Anal.(2017),2474-2492.
39.On the global 2-holonomy for a 2-connection on a 2-bundle,J.Geom.Phys.117(2017)151-178.
40.(With Dongrui Wan)On the quaternionic Monge-Ampere operator,closed positive currents and Lelong-Jensen type formula on quaternionic space,Bull.Sci.Math.141(2017),no.4,267-311.
41.On quaternionic complexes over unimodular quaternionic manifolds,Differential Geometry and its application 58(2018)227-253.
42.The Neumann Problem for the k-Cauchy–Fueter Complex over k-Pseudoconvex Domains in R^4 and the L^2 Estimate,to appear in J.Geom.Anal.
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