References
Catlin, D.: The Bergman kernel and a theorem of Tian. In: Analysis and Geometry in Several Complex Variables, ed. by G. Komatsu, M. Kuranishi. Trends in Math., pp. 1–23. Boston: Birkhäuser 1999
Donaldson, S.K.: Scalar curvature and projective embeddings, I. J. Differ. Geom. 59, 479–522 (2001)
Fujiki, A.: Moduli space of polarized algebraic manifolds and Kähler metrics. Sugaku 42, 231–243 (1990); English translation: Sugaku Expo. 5, 173–191 (1992)
Futaki, A., Mabuchi, T.: Bilinear forms and extremal Kähler vector fields associated with Kähler classes. Math. Ann. 301, 199–210 (1995)
Futaki, A., Mabuchi, T.: Moment maps and symmetric multilinear forms associated with symplectic classes. Asian J. Math. 6, 349–372 (2002)
Gieseker, D.: Global moduli for surfaces of general type. Invent. Math. 43, 233–282 (1977)
Helgason, S.: Differential Geometry and Symmetric Spaces. Pure Appl. Math. 12. New York: Academic Press 1962
Kobayashi, S.: Transformation groups in differential geometry. Berlin, Heidelberg, New York: Springer 1972
Lichnérowicz, A.: Isom��trie et transformations analytique d’une variété kählérienne compacte. Bull. Soc. Math. Fr. 87, 427–437 (1959)
Lübke, M., Teleman, A.: The Kobayashi-Hitchin correspondence. Singapore: World-Scientific 1995
Mabuchi, T.: The Hitchin-Kobayashi correspondence for vector bundles and manifolds. Japanese, Proc. 48th Geometry Symposium, Ibaraki, August 2001, pp. 461–468
Mabuchi, T.: An obstruction to asymptotic semistability and approximate critical metrics. arXiv: math. DG/0404210. To appear in Osaka J. Math. 41 (2004)
Mabuchi, T.: Stability of extremal Kähler manifolds. arXiv: math. DG/0404211. To appear in Osaka J. Math. 41 (2004)
Mabuchi, T.: An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, II. In preparation
Mabuchi, T.: Uniqueness of extremal Kähler metrics for an integral Kähler class. To appear in Int. J. Math.
Mabuchi, T., Nakagawa, Y.: The Bando-Calabi-Futaki character as an obstruction to semistability. Math. Ann. 324, 187–193 (2002)
Mabuchi, T., Weng, L.: Kähler-Einstein metrics and Chow-Mumford stability. Preprint 1998
Mumford, D., Fogarty, J., Kirwan, F.: Geometric invariant theory, 3rd edn. Ergebnisse der Math. und ihrer Grenzgebiete 34, pp. 1–292. Springer 1994
Phong, D.H., Sturm, J.: Scalar curvature, moment maps, and the Deligne pairing. arXiv: math. DG/0209098
Simon, L.: Lectures on geometric measure theory. Austr. Nat. Univ. 3, pp. 1–272, 1983
Tian, G.: The K-energy on hypersurfaces and stability. Commun. Anal. Geom. 2, 239–265 (1994)
Tian, G.: Bott-Chern forms and geometric stability. Discrete Contin. Dyn. Syst. 6, 211–220 (2000)
Tian, G.: On a set of polarized Kähler metrics on algebraic manifolds. J. Differ. Geom. 32, 99–130 (1990)
Tian, G.: Kähler-Einstein metrics with positive scalar curvature. Invent. Math. 130, 1–37 (1997)
Viehweg, E.: Quasi-projective moduli for polarized manifolds. Ergebnisse der Math. und ihrer Grenzgebiete 30, pp. 1–320, Springer 1995
Zelditch, S.: Szegö kernels and a theorem of Tian. Int. Math. Res. Not. 6, 317–331 (1998)
Zhang, S.: Heights and reductions of semi-stable varieties. Compos. Math. 104, 77–105 (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor Yum-Tong Siu on his sixtieth birthday
Rights and permissions
About this article
Cite this article
Mabuchi, T. An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, I. Invent. math. 159, 225–243 (2005). https://doi.org/10.1007/s00222-004-0387-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00222-004-0387-y