The Michigan Mathematical Journal

Scalar curvature behavior for finite-time singularity of Kähler-Ricci flow

Zhou Zhang

Full-text: Open access

Article information

Source
Michigan Math. J. Volume 59, Issue 2 (2010), 419-433.

Dates
First available in Project Euclid: 11 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1281531465

Digital Object Identifier
doi:10.1307/mmj/1281531465

Mathematical Reviews number (MathSciNet)
MR2677630

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 58J35: Heat and other parabolic equation methods

Citation

Zhang, Zhou. Scalar curvature behavior for finite-time singularity of Kähler-Ricci flow. Michigan Math. J. 59 (2010), no. 2, 419--433. doi:10.1307/mmj/1281531465. https://projecteuclid.org/euclid.mmj/1281531465.


Export citation

References

  • H. Cao and X. Zhu, A complete proof of the Poincaré and geometrization conjectures---Application of the Hamilton--Perelman theory of the Ricci flow, Asian J. Math. 10 (2006), 165--492.
  • P. Cascini and G. La Nave, Kähler--Ricci flow and the minimal model program for projective varieties, ArXiv:math/0603064 (math.AG).
  • J.-P. Demailly and M. Paun, Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. (2) 159 (2004), 1247--1274.
  • R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255--306.
  • ------, The formation of singularities in the Ricci flow, Surveys in differential geometry, vol. II (Cambridge, 1993), pp. 7--136, International Press, Cambridge, MA, 1995.
  • S. L. Kleiman, Toward a numerical theory of ampleness, Ann. of Math. (2) 84 (1966), 293--344.
  • B. Kleiner and J. Lott, Notes on Perelman's papers, Geom. Topol. 12 (2008), 2587--2855.
  • J. Kollar and S. Mori, Birational geometry of algebraic varieties, with the collaboration of C. H. Clemens and A. Corti [translated from the 1998 Japanese original], Cambridge Tracts in Math., 134, Cambridge Univ. Press, Cambridge, 1998.
  • R. Lazarsfeld, Positivity in algebraic geometry. I. Classical setting: Line bundles and linear series, Ergeb. Math. Grenzgeb. (3), 48, Springer-Verlag, Berlin, 2004.
  • J. Morgan and G. Tian, Ricci flow and the Poincaré conjecture, Clay Math. Monogr., 3, Amer. Math. Soc., Providence, RI, 2007.
  • N. Sesum, Curvature tensor under the Ricci flow, Amer. J. Math. 127 (2005), 1315--1324.
  • N. Sesum and G. Tian, Bounding scalar curvature and diameter along the Kähler Ricci flow (after Perelman), J. Inst. Math. Jussieu 7 (2008), 575--587.
  • J. Song and G. Tian, The Kähler--Ricci flow on surfaces of positive Kodaira dimension, Invent. Math. 170 (2007), 609--653.
  • G. Tian, New results and problems on Kähler--Ricci flow, Astérisque 322 (2008), 71--92.
  • G. Tian and Z. Zhang, On the Kähler--Ricci flow on projective manifolds of general type, Chinese Ann. Math. Ser. B 27 (2006), 179--192.
  • Y. Zhang, Miyaoka--Yau inequality for minimal projective manifolds of general type, Proc. Amer. Math. Soc. 137 (2009), 2749--2754.
  • Z. Zhang, Degenerate Monge--Ampère equations over projective manifolds, Ph.D. thesis, MIT, 2006.
  • ------, Scalar curvature bound for Kähler--Ricci flows over minimal manifolds of general type, Int. Math. Res. Not. 20 (2009), 3901--3912.