Constrained matrix Li-Yau-Hamilton estimates on Kähler manifolds
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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 Classification53C44 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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