Skip to main content
SpringerLink
Log in

Matrix Li-Yau-Hamilton estimates for the heat equation on Kähler manifolds

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bando, S.: On classification of three-dimensional compact Kähler manifolds of nonnegative bisectional curvature. J. Differential Geom. 19, 283–297 (1984)

    MATH  Google Scholar 

  2. Bishop, R.L., Goldberg,S.I.: On the second cohomology group of a Kähler manifold of positive curvature. Proceedings of AMS. 16, 119–122 (1965)

    MATH  Google Scholar 

  3. Cao, H.-D.: Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds. Invent. Math. 81, 359–372 (1985)

    MATH  Google Scholar 

  4. Cao H.-D.: On Harnack’s inequalities for the Kähler-Ricci flow. Invent. Math. 109, 247–26 (1992)

    Google Scholar 

  5. Greene, R.-E., Wu, H.: On Kähler manifolds of positive bisectional curvature and a theorem of Hartogs. Abh. Math. Sem. Univ. Hamburg 47, 171–185 (1978)

    MATH  Google Scholar 

  6. Hamilton, R.S.: Four-manifolds with positive curvature operator. J. Differential Geom. 24, 153–179 (1986)

    MATH  Google Scholar 

  7. Hamilton, R.: A matrix Harnack estimate for the heat equation. Comm. Anal. Geom. 1, 113–126 (1993)

    MATH  Google Scholar 

  8. Li, P., Tam, L.-F.: The heat equation and harmonic maps of complete manifolds. Invent. Math. 105, 1–46 (1991)

    MathSciNet  Google Scholar 

  9. Li, P., Wang, J.: Comparison theorem for Kähler manifolds and positivity of spectrum. preprint

  10. Li, P., Yau, S.-T.: On the parabolic kernel of the Schrödinger operator. Acta Math. 156, 153–201 (1986)

    MathSciNet  Google Scholar 

  11. Mok, N.: The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature. J. Differential Geom. 27, 179–214 (1988)

    MATH  Google Scholar 

  12. Mok, N., Siu, Y.T., Yau, S.T.: The Poincaré-Lelong equation on complete Kähler manifolds. Compositio Math. 44, 183–218 (1981)

    MATH  Google Scholar 

  13. Ni, L.: A new matrix Li-Yau-Hamilton estimate for Kähler-Ricci flow. submitted

  14. Ni, L., Tam, L.-F.: Plurisubharmonic functions and Kähler Ricci flow. Amer. J. Math. 125, 623–645 (2003)

    MATH  Google Scholar 

  15. Ni, L., Tam, L.-F.: Louville properties of plurisubharmonic functions. Unpublished preprint, arXiv: math. DG/0212364

  16. Ni, L., Tam, L.-F.: Kähler Ricci flow and Poincaré-Lelong equation. Comm. Anal. Geom. 12, 111–141 (2004)

    MathSciNet  Google Scholar 

  17. Ni, L., Tam, L.-F.: Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature. J. Differential Geom. 64, (2003) 457–524

  18. Perelman, G.: The entropy formula for the Ricci flow and its geometric applications. arXiv: math.DG/ 0211159

  19. Shi, W.X.: Ricci deformation of metric on complete noncompact Kähler manifolds, Ph. D. thesis at Harvard University, 1990

Download references

Author information

Author notes

  1. Huai-Dong Cao

    Present address: Department of Mathematics, Lehigh University, Bethlehem, PA, 18015, USA

Authors and Affiliations

  1. Institute for Pure and Applied Mathematics, Los Angeles, CA, 90095-7121, USA

    Huai-Dong Cao

  2. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093, USA

    Lei Ni

  3. Department of Mathematics, Texas A&M University, College Station, TX, 77843, USA

    Huai-Dong Cao

Authors
  1. Huai-Dong Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lei Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huai-Dong Cao.

Additional information

Research partially supported by NSF grant DMS-0206847.

Research partially supported by NSF grant DMS-0203023.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cao, HD., Ni, L. Matrix Li-Yau-Hamilton estimates for the heat equation on Kähler manifolds. Math. Ann. 331, 795–807 (2005). https://doi.org/10.1007/s00208-004-0605-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00208-004-0605-3

Keywords

Search

Navigation