0;136;0c0;136;0c0;136;0c
Bibliography of pertinent literature
Bibliography of pertinent literature
Zhuang-dan Guan
- (with M. X. Liang)Complete Co-homogeneity One Kahler Metrics on the Affine Quadric of Complex Dimension Two(related to a
Cohomogeneity
One Point of View of A Yau Conjecture)II---New Hyperkahler Metrics, in preprint 2024, 47 pages and submitted
- 1. (with N. Li, Z. Wang)Some remarks on existence of a complex structure on the compact six sphere, Axioms 13(2024), art. 719.
doi: 10.3390/axioms13100719
- (with J. Chen, Y. Y. Tang)The calculations of holomorphic bisectional curvatures of a co-homogeneity one K\"ahler metric on
type III domains, in preprint 2023, 12 pages and submitted
- (with J. Chen, S. J. Jing, Y. Y. Tang)The Extremal Metric on A Class of Twisted Fock-Bargmann-Hartog Domains, 10 pages, in preprint 2023 and submitted
- 2. Some Applications of Group Actions in Complex Geometry, Chin. Quart. J. Math. 38 (2023), 254--275.
doi: 10.13371/j.cnki.chin.q.j.m.2023.03.002 MR 4770654
- 3. (with M. X. Liang)Complete Co-homogeneity One Kahler Metrics on the Affine Quadric of Complex Dimension Two(related to a
Cohomogeneity
One Point of View of A Yau Conjecture), Chin. Quart. J. Math. 39 (2024), 200--220.
doi: 10.13371/j.cnki.chin.q.j.m.2024.02.008
- (with J. Chen)Generalized Maxwell-Einstein Metrics on Completions of Certain
Line Bundles, 63 pages, in preprint and submitted 2024
- (with J. Chen)Generalized Maxwell-Einstein Metrics on Completions of Certain
Line Bundles II, in preparation
- 4. (with J. Chen)Existence of Some Special Conformally K\"ahler Metrics on Certain CP^1 bundles, 22 pages, accepted and to appear in Acta
Mathematica Scientia 2025
- 5. (with M. X. Liang)Complete Kahler Metrics with Positive Holomorphic Sectional Curvatures on
Certain Line Bundles(related to a Cohomogeneity One Point of
View of A Yau Conjecture)--II, 16 pages, accepted and to appear in Acta Mathematica Sinica
- 6. (with X. M. Duan)Complete Kahler Metrics with Positive Holomorphic Sectional Curvatures on
Certain Line Bundles(relatd to a Cohomogeneity One Point of
View of A Yau Conjecture), Acta. Math. Scientia, vol. 44B (2024), pp.78--102.
doi: 10.1007/s10473-024-0103-5.
- 7. Maxwell-Einstein Metrics on Completions of Certain C* Bundles, Acta Mathematica Scientia 43B(2023), p. 363---372.
doi: 10.1007/s10473-023-0120-9. MR 4498386
- 8. (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.
- 9. 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 MR 4756779
- 10. Type II Compact Almost Homogeneous Manifolds of Cohomogeneity One---II,
Intern. J. Math. 30(2019), No. 13, Article 1940002.
doi: 10.1142/S129167X19400020. IJM10
- 11. Nonexistence of S^6 type Threefolds, Pacific J. of Math. 305(2020),
p. 641--644.doi: 10.2140/pjm.2020.305.641
- 12. (with P. Orellana and A. Van)
Type I Compact Almost Homogeneos Manifolds of Cohomogeneity One---IV
Axioms 8(2019), no. 1, art. 2.
- 13. 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.
- 14. A Classification of Compact Cohomogeneity One Locally Conformal K\"ahler Manifolds,
Mathematics 12(2024), no. 11, art. 1710. doi: 10.3390/math12111710.
- 15. 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.
- 16. (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. IJM9
- 17. (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. IJM8
- Modification and the Cohomology Groups of Compact Solvmanifolds II, in preprint and submitted 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.
- 18. On Bisectional Negatively Curved Compact K\"ahler-Einstein Surfaces, Pacific Journal of Mathematics 288 (2017),
343--353.
- 19. Positive Lemma, Generalized Extremal-solitons and Second Order Linear
Differential Equations, Advancement and Development in Mathematical Science, vol 1 (2012), issue 2, 13--32.
- 20. 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.
- 21. On Classification of Compact Complex Solvmanifolds,
doi: 10.1016/j.jalgebra.2011.08.026, J. of Algebra, vol 347 (2011), 69--82.
- 22. Toward a Classification of Symplectic
Nilmanifolds, International Mathematical Research Notices,
vol 2010 (2010), 4377--4384
2010:doi:10.1093/imrn/rnq049.
- 23. 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.
doi:10.2478/s11533-008-0055-3
- 24. 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
- 25. 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.
- 26. 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.
- 27. 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).
- 28. 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).
- 29. 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.
- 30. 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.
- 31. 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.
- 32. 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.
- 33. 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.
- 34. 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
- 35. On the Betti Numbers of Irreducible Compact Hyperk\"ahler Manifolds
of Complex Dimension Four, Math. Res. Letters vol 8 (2001), 663--669.
- 36. 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.
- 37. (with X. Chen) Existence of Extremal Metrics on Almost
Homogeneous Manifolds
of Cohomogeneity One, Asian J. Math. vol 4 (2000), 817--830..
- 38. 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
- 39. 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 IJM7
- 40. 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.
- 41. 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.
- 42. Classification of Compact Complex Homogeneous
Spaces with Invariant Volumes,
Transactions of AMS. 354(2002) 4493-4504.
42' Announcement
appeared in ERA-AMS vol 3 (1997), 90-92.
- 43. Classification of Compact Homogeneous Spaces with
Invariant Symplectic Structures,
ERA-AMS vol 3 (1997), 52-54.
- 44. Toward a Classification of Almost Homogeneous Manifolds
II---Bad Models, International J. Math., vol 10 (1999), 571--586. IJM6
- 45. Toward a Classification of Almost Homogeneous Manifolds
III---SL(2)xC* Actions, International J. Math., vol 11 (2000), 799--809. IJM5
- 46. A Splitting Theorem for Compact Complex
Homogeneous Space with a
Symplectic Structure, Geometrica Dedicata vol. 63(1996), 217-225.
MR 98a:53105.
- 47. 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.
- 48. Examples of Holomorphic Symplectic Manifolds which admit no K\"ahler
Structure III, International J. of Math. vol. 6(1995), 709-718. MR
97i:32034. IJM4
- 49. 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.
- 50. Existence of Extremal Metrics on Almost Homogeneous Spaces with Two Ends.
Transaction of AMS, vol. 347(1995), 2255-2262.
- 51. Quasi-Einstein Metrics, International J. of Math., vol. 6(1995), 371-379. MR 96e:53060. IJM3
- 52. Stablity of Hermitian Vector Bundles, a Quantitative Point of View,
Intern'l J. Math. 3 (1992), 477-481. MR 93k:32067. IJM2
- 53. Toward a Classification of Almost Homogeneous Manifolds
I---Linearization of the Singular Extremal Rays. International J. of
Math., vol 8(1997), 999-1014. IJM1
- 54. (with Dorfmeister) Fine Structures of Reductive
Pseudo-K\"ahlerian
Spaces, Geometrica Dedicata 39 (1991), 321-338. MR 92h:53081.
54' Supplement in Geom. Dedi. 42 (1992), 241-242.
- 55. (with Dorfmeister) Pseudo-K\"ahlerian Homogeneous
Spaces Admitting a
Reductive Transitive Group of Automorphisms, Math. Zeitschrift
209 (1992), 89-100. MR 92k:32058.
- 56. (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).
- 57. (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).
- 58. 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