关庄丹203
姓名：关庄丹
职称：教 授
办公室：F206
邮箱： guan@henu.edu.cn
研究方向：复几何和微分几何，齐性空间
教育背景：
1990.09-1993.06， 博士， 加州大学伯克来分校， 基础数学专业
1983.09-1986.06， 硕士， 中国科学院大学， 基础数学专业
1978.10-1982.06， 学士， 厦门大学， 基础数学专业
工作经历：
2019.01至今， BEVITOR伟德APP官网， 教授
2018.09-2018.12 BEVITOR伟德APP官网， 访问教授
2004.07-2018.11，加州大学， 副教授
2000.07-2004.07, 加州大学， 助理教授
1993.07-2000.06，普林斯顿大学， 助理教授及副教授
代表性学术论文：
[1]D. Guan, On Some Recent Progress in Complex Geometry---the Area Related to Homogeneous Manifolds, Chinese Quart. J. of Math. 35(2020), p. 111--144. doi: 10.13371/j.cnki.chin.q.j.m.2020.02.001. See also 1 and 2
[2]D. Guan, Type II Compact Almost Homogeneous Manifolds of Cohomogeneity One---II, Intern. J. Math. 30(2019), No. 13, Article 1940002. doi: 10.1142/S129167X19400020.
论文
(with J. Chen)On Generalized Maxwell-Einstein Metrics, in preparation
Maxwell-Einstein Metrics on Completions of Certain C* Bundles, accepted and to appear in Acta Mathematica Scientia (2023)
(with Z. H. Wang)A Note on the Nonexistence of A Complex Threefold As A Conjugate Orbit of G2, Results in Math. 77(2022), Article 139. doi: 10.1007/s00025-022-01678-5.
On Some Recent Progress in Complex Geometry---the Area Related to Homogeneous Manifolds, Chinese Quart. J. of Math. 35(2020), p. 111--144. doi: 10.13371/j.cnki.chin.q.j.m.2020.02.001. See also 1 and 2
Type II Compact Almost Homogeneous Manifolds of Cohomogeneity One---II, Intern. J. Math. 30(2019), No. 13, Article 1940002. doi: 10.1142/S129167X19400020.
Nonexistence of S^6 type Threefolds, Pacific J. of Math. 305(2020), p. 641--644.doi: 10.2140/pjm.2020.305.641
(with P. Orellana and A. Van) Type I Compact Almost Homogeneos Manifolds of Cohomogeneity One---IV Axioms 8(2019), no. 1, art. 2.
A New Proof of A Conjecture on Nonpositive Ricci Curved K\"ahler-Einstein Surfaces Mathematics 6(2018), no. 2, art. 21. doi: 10.3390/math6020021.
A Classification of Compact Cohomogeneity One Locally Conformal K\"ahler Manifolds, preprint 2017, 12 pages.
A Note on the Classification of Compact Complex Homogeneous Locally Conformal K\"ahler Manifolds Journal of Mathematics and Statistics 13(2017), no. 3. p. 261--267. doi: 10.3844/jmssp.2017.261.267.
Examples of Simply Connected Holomorphic Symplectic Manifolds which are not Formal I, in preprint 2015; 13 pages.
(with P. Cernea) Killing Fields Generated by Multiple Solutions to the Fischer-Marsden Equation Intern. J. Math. 26 (2015), no. 4. doi: 10.1142/S0129167X15400066.
(with P. Cernea) Killing Fields Generated by Multiple Solutions to the Fischer-Marsden Equation II Intern. J. Math. 27 (2016), no. 10. doi: 10.1142/S0129167X16500804.
Modification and the Cohomology Groups of Compact Solvmanifolds II, in preprint 2013
Classification of Real Eight Dimensional Compact Solvmanifolds with Real Symplectic Structures, in preparation 2013
m-extremal metrics and m-Calabi flows, in preparation 2012.
On Bisectional Negatively Curved Compact K\"ahler-Einstein Surfaces, Pacific Journal of Mathematics 288 (2017), 343--353.
Positive Lemma, Generalized Extremal-solitons and Second Order Linear Differential Equations, Advancement and Development in Mathematical Science, vol 1 (2012), issue 2, 13--32.
Toward a classification of compact real solvmanifolds with real symplectic structures, Journal of Algebra 379 (2013), 144--155. doi: 10.1016/j.algebra.2013.01.011.
On Classification of Compact Complex Solvmanifolds, doi: 10.1016/j.jalgebra.2011.08.026, J. of Algebra, vol 347 (2011), 69--82.
Toward a Classification of Symplectic Nilmanifolds, International Mathematical Research Notices, vol 2010 (2010), 4377--4384 2010:doi:10.1093/imrn/rnq049.
Affine Compact Almost-Homogeneous Manifolds of Cohomogeneity One Central European Journal of Mathematics, vol 7 (2009), 84--123. Note: Theorem 10.2 is true when the manifold is Fano, cohomogeneity one and has a semisimple automorphism group.
Classification of Compact Complex Homogeneous Manifolds with Pseudo-k\"ahlerian Structures, Jour. of Algebra, vol 324 (2010), 2010--2024; doi:10.1016/j.jalgebra.2010.06.013
Classification of Compact Homogeneous Manifolds with Pseudo-k\"ahlerian Structures (Announcement) Comptes Rendus Math\'ematiques de l'Acad. Sci. Canada, vol 31 (2009), no. 1. 20--23.
Modification and the Cohomology Groups of Compact Solvmanifolds, ERA-AMS 13 (2007), 74--81; see also Comments
A Complete Classification of Compact Almost Homogeneous K\"ahler Manifolds of Cohomogeneity One with a Higher Codimensional End, in preparation.
Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---I, Pacific J. of Appl. Math., vol 3 (2011), 43--72(Original proof Jan. 20, 2011).
Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---II, Pacific J. of Appl. Math., vol 3 (2011), 179--202(Original proof Jan. 21, 2011).
Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---III, Pacific J. of Mathematics, vol. 261 (2013), 369--388; doi:10.2140/pjm.2013.261.369.
Type II Compact Almost Homogeneous Manifolds of Cohomogeneity One, Pacific J. of Mathematics, vol. 253 (2011), 383--422; doi:10.2140/pjm.2011.253.383.
Moser Vector Fields and Geometry of the Mabuchi Moduli Space of K\"ahler Metrics, Geometry, 2014 (2014), article 968064.
Jacobi Fields and the Geodesic Stability, in preparation.
Book cooperated with S. Kobayashi: Compact Complex Manifolds and K\"ahler Geometry, in process.
Testing the Geodesic Stability on Toric Bundles, in preparation.
Extremal-Solitons and Exponential C^{\infty} Convergence of Modified Calabi Flow on Certain CP^1 bundles, Pacific J. Math. vol. 233 (2007), 91-124; doi:10.2140/pjm.2007.233.91.
Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---IV, Ann. Glob. Anal. Geom. 30(2006), 139--167.
An Inequality of Rozansky-Witten Invariants, in preparation.
On Representation Theory and the Cohomology Rings of Irreducible Compact Hyperk\"ahler Manifolds of Complex Dimension Four, Central European Journal of Mathematics, vol 1 (2003), 661--669. See also original tex file
On the Betti Numbers of Irreducible Compact Hyperk\"ahler Manifolds of Complex Dimension Four, Math. Res. Letters vol 8 (2001), 663--669.
On Modified Mabuchi Functional and Mabuchi Moduli Spaces of K\"ahler Metrics on Toric Bundles. Math. Research Letters vol 6 (1999), 547--555.
Quasi-Einstein Metrics and Evolution of Metrics in a K\"ahler Class, a preprint will come out soon.
(with X. Chen) Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One, Asian J. Math. vol 4 (2000), 817--830..
Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---II, Journal of Geometric Analysis, vol 12 (2002), 63--79. The final version before publication
Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---III, International Journal of Mathematics, vol 14 (2003), 259--287. The final version before publication Note written on Feb. 14, 2007: The original paper was cut by the referees and the editors. Therefore, some information in the paper was missing. Here I found a pdf copy of an original source which was modified after receiving two preprints from Andrew Spiro and further discussions. It is apparently that the completion of the normal bundle of the exceptional divisor in section 6 is different from the projective normal bundle and our degeneration (if it actually exists) is a little different from that in the recent paper of J. Ross and R. P. Thomas (JDG 72 (2006), 429--466). Our condition is stronger than theirs.
Toward a Classification of Compact Complex Homogeneous Manifolds, Journal of Algebra vol. 273 (2004), 33--59; doi:10.1016/j.jalgebra.2003.11.007.
Toward a Classification of Compact Complex Homogeneous Manifolds II, in preparation.
On Compact Symplectic Manifolds with Lie Group Symmetries, Transactions of AMS. 357 (2005), 3359-3373.
Classification of Compact Contact Homogeneous Spaces, a preprint will come out soon.
Classification of Compact Complex Homogeneous Spaces with Invariant Volumes, Transactions of AMS. 354(2002) 4493-4504. Announcement appeared in ERA-AMS vol 3 (1997), 90-92.
Classification of Compact Homogeneous Spaces with Invariant Symplectic Structures, ERA-AMS vol 3 (1997), 52-54.
Toward a Classification of Almost Homogeneous Manifolds II---Bad Models, International J. Math., vol 10 (1999), 571--586.
Toward a Classification of Almost Homogeneous Manifolds III---SL(2)xC* Actions, International J. Math., vol 11 (2000), 799--809.
A Splitting Theorem for Compact Complex Homogeneous Space with a Symplectic Structure, Geometrica Dedicata vol. 63(1996), 217-225. MR 98a:53105.
Examples of Holomorphic Symplectic Manifolds which admit no K\"ahler Structure II, Invent. Math. vol. 121(1995), 135-145. (see also F. Bogomolov: On Guan's Examples of Simply Connected Non-K\"ahler Compact Complex Manifolds, Amer. J. Math. 118(1996), 1037-1046). MR 97i:32033.
Examples of Holomorphic Symplectic Manifolds which admit no K\"ahler Structure III, International J. of Math. vol. 6(1995), 709-718. MR 97i:32034.
Examples of Compact Holomorphic Symplectic Manifolds Which Are Not K\"ahlerian, (In Geometry and Analysis on Complex Manifolds---Festschift for Professor S. Kobayashi's 60-th birthday, World Scientific Publishing Co. 1994), 63-74.
Existence of Extremal Metrics on Almost Homogeneous Spaces with Two Ends. Transaction of AMS, vol. 347(1995), 2255-2262.
Quasi-Einstein Metrics, International J. of Math., vol. 6(1995), 371-379. MR 96e:53060.
Stablity of Hermitian Vector Bundles, a Quantitative Point of View, Intern'l J. Math. 3 (1992), 477-481. MR 93k:32067.
Toward a Classification of Almost Homogeneous Manifolds I---Linearization of the Singular Extremal Rays. International J. of Math., vol 8(1997), 999-1014.
(with Dorfmeister) Fine Structures of Reductive Pseudo-K\"ahlerian Spaces, Geometrica Dedicata 39 (1991), 321-338. MR 92h:53081.
(with Dorfmeister) Pseudo-K\"ahlerian Homogeneous Spaces Admitting a Reductive Transitive Group of Automorphisms, Math. Zeitschrift 209 (1992), 89-100. MR 92k:32058.
(with Dorfmeister) Classification of Compact Homogeneous Pseudo-K\"ahler Manifolds, Comm. Math. Helv. 67 (1992), 499-513. MR 93i:32042.(see also Huckleberry A. L.: Homogeneous Pseudo-K\"ahlerian Manifolds: A Hamiltonian Viewpoint, Note di Matematica 10(1990) suppl. 2. 337-342. MR 94f:53052).
(with Y. Hong and H. C. Yang) A Remark on K\"ahler-Einstein Manifolds, Acta Math. Sinica 31 (1988), 595--602. MR 0983430 (90c:53171).
Curvature on the Hermitian Symmetric Spaces. Acta Math. Sinica. New Series 4 (1988), 270-283.
Zhuang-dan Guan, Department of Mathematics, University of California at Riverside, Riverside, CA 92521, U.S.A.
e-mail: zguan@math.ucr.edu and guan@henu.edu.cn
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科研项目：
1. 项目名称（编号），美国国家科学基金项目，2001/07-2005/08，已结题，主持；
2. 项目名称:一些特殊的复几何结构理论及多复变函数论,编号:12171140，国家自然科学基金面上项目，2022/01-2025/12，51万元，主持。
主讲课程：
2021年春:黎曼几何，2021秋:代数几何，2022年春:复几何，2022年秋:黎曼流形上的分析。
学术交流：
1. 2021年07月受邀在厦门大学做关于实六维球面上复结构的报告；
荣誉与奖励:
1996年 获NSF Fellowship奖项
1989年 获优秀博士生Fellowship奖
Name：Guan, Zhuang-dan Daniel
Title：Prof. Dr.
Office：F206
Email： guan@henu.edu.cn
Research Field：Complex Geometry, Differential Geometry and Homogeneous Spaces
Education：
1990.09-1993.06, Ph.D.， University of California at Berkeley
1983.09-1986.06, Master of Science, Institute of Mathematics, Academic Sininca, Beijing, China
1978.10-1982.06, Bachelor of Science, Xiamen University, Xiamen, China
Position：
2019.01-， Henan University，Professor
2004.07-2018.11, University of California at Riverside, Associate professor
2018.09-2018.12, Henan University, Visiting Professor
1993.09-2004.07, Princeton University and University of California at Riverside, Assistant professor
Selected publications：
[1]D. Guan, Examples of compact holomorphic symplectic manifolds which are not
Kählerian II, Invent Math. 121 (1995), 135-145.
[2]D. Guan, On the Betti Numbers of Irreducible Compact Hyperkähler Manifolds of Complex Dimension Four, Mathematical Research Letters 8 (2001), 663-669.
Research Funding：
1. D. Guan，National Natural Science Foundation of USA(XXX)，2001.07-2005.08, PI
2. D. Guan, National Natural Science Foundation of China
Teaching：
Algebraic Geometry, Fall 2021
Talks：
1. 2021.07, Xiamen University,；
Honor and awards
Excellent Fellowship, NSF Fellowship