Mathematische Annalen

, Volume 361, Issue 3–4, pp 927–941 | Cite as

Constrained matrix Li-Yau-Hamilton estimates on Kähler manifolds

  • Xin-An RenEmail author
  • Sha Yao
  • Li-Ju Shen
  • Guang-Ying Zhang


We derive a family of constrained matrix Li-Yau-Hamilton estimates on Kähler manifolds. As a result, we first get a constrained matrix Li-Yau-Hamilton estimate for heat equation on a Kähler manifold with fixed Kähler metric. Secondly, we get such estimate for forward conjugate heat equation on Kähler manifolds with time dependent Kähler metrics evolving under the Kähler-Ricci flow.

Mathematics Subject Classification

53C44 53C55 



The first named author would like to thank Professors Q.-K. Lu, S.-K. Wang and K. Wu for valuable discussions and comments. He would also like to thank Professor H.-W. Xu for helpful suggestions. This work is partially supported by the Fundamental Research Funds for Central Universities (Grant No. 2012QNA40).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Xin-An Ren
    • 1
    Email author
  • Sha Yao
    • 1
  • Li-Ju Shen
    • 1
  • Guang-Ying Zhang
    • 1
  1. 1.Department of MathematicsChina University of Mining and TechnologyXuzhouChina

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