基本介紹
- 中文名：王宏玉
- 國籍：中國
- 民族：漢族
- 職業：數學家
- 性別：男
人物經歷,研究方向,主要貢獻,發表文章,
人物經歷
南京大學，1978-1982，數學系本科生，計算數學專業，於1982年1月獲學士學位。
1988 年末與世界著名數學家 Uhlenbeck 各自獨立構造了不穩定 Yang-Mills 場，並因此應邀去美國哈佛大學數學系做兩年博士後，然後去杜克訪問一年。
2001 年 9 月被南京大學聘為客座教授，並任南京大學兼職博士生導師。
研究方向
主要從事度量幾何、辛幾何和非線性發展方程的研究。
主要貢獻
與梅加強等合作給出了 R (n>= 3) 極小體積為零的詳細證明。
系統地研究了閉流形的微分同胚群與保體積微分同胚群之間的關係, 對著名的 J. Morse 定理給出了另一種證明; 並研究了辛流形上的廣義 Calabi-Yau 方程。
給出了 Floer 同調的正合序列定理;
與北京大學丁偉岳, 中科院王友德合作研究了 Schrödinger flow, 深入地 研究了取值於 Hermite 對稱空間的廣義 Heisenberg 模型和相伴於緊 Hermite 李代數的三次非線性 Schrödinger 方程, 給出了兩者之間的一一對應, 並由此構造了具體的周期解. 還證明了 Schrödinger 流的整體解的存在性。
系統深入地研究了 Yang-Mills 場及其方程, 探討了 R 上經典 Yang-Mills 場的模空間幾何, 為 Yang-Mills 方程構造了無窮多個非極小解, 亦即為不穩定 Yang-Mills 方程構造了無窮多個非極小解, 亦即為不穩定 Yang-Mills 場建立了存在性定理, 此結果被收入美國大學物理專業研究生教科書。
發表文章
Wang, Hong Yu; Zhu, Peng 2010
On a generalized Calabi-Yau equation.
Annales l'Institut Fourire, 60 (2010), no. 5, 1595--1615.
Wang, Hong Yu; Zhu, Peng 2010
Local Riemann-Roch theorem for almost Hermitian manifolds.
Bull Braz Math Soc, 41 (2010), no. 4, 583--605.
Luo, Jin Quan; Tang, Yuan Sheng; Wang, Hong Yu 2010
Cyclic Codes and Sequences: The Generalized Kasami Case.
IEEE Transactions on Infomation Theory, 56 (2010), no. 5, 2130--2142.
Wang, Hong Yu; Zhu, Xiu Juan 2009
On initial data of the monopole equation.
Acta Math. Sinica (English series), 25 (2009), no. 12, 2127--2132.
Wang, Hong Yu; Xu, Hai Feng 2009
Minimal volume of the connected sum of Euclidean spaces,
Differential Geometry - Dynamical Systems. 11 (2009), 185--194.
Mei, Jia Qiang; Wang, Hong Yu; Xu, Hai Feng 2008
An elementary proof of MinVol(R)=0 for n>=3,
An. Acad. Brasil. Ciênc. 80 (2008), no. 4, 597--616.
Ding, Wei Yue; Wang, Hong Yu; Wang, You De 2003
Schrödinger flows on compact Hermitian symmetric spaces and related problems.
Acta Math. Sin. (Engl. Ser.) 19 (2003), no. 2, 303--312. (Reviewer: Shu-Cheng Chang)
Wang, Hong Yu 2002
Nonlinear Schrödinger systems associated with Hermitian symmetric Lie algebras.
Differential geometry and related topics, 237--249, World Sci. Publ., River Edge, NJ, 2002.
Wang, Hong Yu 2002
Geometric nonlinear Schrödinger equations.
Integrable systems, topology, and physics (Tokyo, 2000), 313--324,
Contemp. Math., 309, Amer. Math. Soc., Providence, RI, 2002. (Reviewer: Leung-Fu Cheung)
Pang, Peter Y. H.; Wang, Hong Yu; Wang, You De 2002
Schrödinger flow on Hermitian locally symmetric spaces.
Comm. Anal. Geom. 10 (2002), no. 4, 653--681. (Reviewer: Shu-Cheng Chang)
Wang, Hong Yu; Wang, You De 2002
Global nonautonomous Schrödinger flows on Hermitian locally symmetric spaces.
Sci. China Ser. A 45 (2002), no. 5, 549--561. (Reviewer: Shu-Yu Hsu)
Dai, Bo; Wang, Hong Yu 2002
A note on diffeomorphism groups of closed manifolds.
Ann. Global Anal. Geom. 21 (2002), no. 2, 135--140. (Reviewer: Nikolai K. Smolentsev)
Pang, P. Y. H.; Wang, H. Y.; Yin, J. X. 2002
Free-boundary problem for a singular diffusion equation.
J. Math. Anal. Appl. 265 (2002), no. 2, 414--429.
Pang, Peter Y. H.; Wang, Hong Yu; Wang, You De 2001
Schrödinger flow for maps into Kähler manifolds.
Asian J. Math. 5 (2001), no. 3, 509--533.
Wang, Hong Yu; Wang, You De 2000
Global inhomogeneous Schrödinger flow.
Internat. J. Math. 11 (2000), no. 8, 1079--1114. (Reviewer: Kuppuswamy Porsezian)
Pang, Peter Y. H.; Wang, Hong Yu; Wang, You De 2000
Local existence for inhomogeneous Schrödinger flow into Kähler manifolds.
Acta Math. Sin.(Engl. Ser.) 16 (2000), no. 3, 487--504. (Reviewer: Knut Smoczyk)
Li, H. L.; Pang, P. Y. H.; Wang, H. Y.; Yin, J. X. 1999
On a partial differential equation arising in electrodiffusion in thin-film conductors.
J. Math. Anal. Appl. 232 (1999), no. 1, 20--33.
Wang, Hong Yu 1997
The exactness theorem for Floer homology.
Publ. Res. Inst. Math. Sci. 33 (1997), no. 5, 713--750. (Reviewer: David E. Hurtubise)
Wang, Hong Yu 1997
Morse theory and non-minimal solutions to the Yang-Mills equations.
Tsukuba J. Math. 21 (1997), no. 3, 567--593.
Wang, Hong Yu 1995
Remarks on the moduli spaces over S.
Far East J. Math. Sci. 3 (1995), no. 2, 229--245. (Reviewer: Antony Maciocia)
Wang, Hong Yu 1992
The construction of isolated reducible SU(2)-connections over S X S.
Acta Math. Sinica (N.S.) 8 (1992), no. 1, 60--77. (Reviewer: Xiao Wei Peng)
Wang, Hong Yu 1991
The existence of nonminimal solutions to the Yang-Mills equation with group SU(2) on S X S and S X S.
J. Differential Geom. 34 (1991), no. 3, 701--767. (Reviewer: Jan Segert)
Wang, Hong Yu 1984
A perturbation theorem and stability for a surface with prescribed mean curvature. (In Chinese)
Nanjing Daxue Xuebao Shuxue Bannian Kan 1 (1984), no. 2, 189--209. (Reviewer: C.-C. Hsiung)
