Plurisubharmonic functions and the Kähler-Ricci flow

By Lei Ni, Luen-Fai Tam. 2002

51 citations recorded by the source corpus.

In this paper, a sharp linear trace Li-Yau-Hamilton inequality for Kahler-Ricci flow is proved. The new inequality extends the previous trace Harnack inequality obtained by H.-D. Cao. We also establish sharp gradient estimates for the positive solution of the time-dependent heat equation for some cases. Finally, we apply this new linear trace Li-Yau-Hamilton inequality to study the Liouville properties of the plurisubharmonic functions on complete Kahler manifolds with bounded nonnegative holomorphic bisectional curvature.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0ce00888ff3b316767c6b574cd6028e6e18bc31d

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

A matrix Li-Yau-Hamilton estimate for Kähler-Ricci flow (2007, methodology): “Following [ NT1 ], We called our estimate in [CN] a Li-Yau-Hamilton estimate (or inequality, which is also referred as differential Harnack inequality in some literatures).”
Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature (2003, unknown): “Hence η = ρ − √ −1∂ ¯ ∂w = √ −1∂ ¯ ∂(Ψ − w) satisfies (2.1) by Lemma 2.1 in [ 37 ].”