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

By Huaihuo Cao, Lei Ni. 2002

90 citations recorded by the source corpus.

In [L-Y], Peter Li and S.-T. Yau developed the fundamental gradient estimate, which is now widely called the Li-Yau estimate, for any positive solution u(x, t) of the heat equation on a Riemannian manifold M(n = dimRM) and showed how the classical Harnack inequality can be derived from their gradient estimate. When M is complete and of nonnegative Ricci curvature, the Li-Yau estimate is sharp. Later in [H2], Richard Hamilton extended the Li-Yau estimate to the full matrix version of the Hessian estimate of u under the stronger assumptions that M is Ricci parallel and of nonnegative sectional curvature. In this paper, we consider positive solutions to the heat equation ( ∂

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

View Paper: https://www.semanticscholar.org/paper/58183b8a7950bafd47531918d6c4ca03552ccdb9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Xiaodong Cao
2. R. Hamilton
3. Qi S. Zhang
4. Huaihuo Cao

In Astronomy and Astrophysics

1. R. Hamilton
2. Xiaodong Cao
3. Huaihuo Cao

In Geometry and Topology

1. R. Hamilton
2. Xiaodong Cao
3. Qi S. Zhang
4. Huaihuo Cao

Citations in the corpus

• Differential Harnack Estimates for Time-Dependent Heat Equations with Potentials (2008, methodology): “The fundamental solution and Harnack inequality of time-dependent heat equation have also been studied by C. Guenther [Gue02]. In [ CN05 ], H.-D.”