Matrix Li-Yau-Hamilton estimates under Ricci Flow and parabolic frequency
- Resource Type
- Working Paper
- Authors
- Li, Xiaolong; Zhang, Qi S.
- Source
- Subject
- Mathematics - Differential Geometry
Mathematics - Analysis of PDEs
53E20, 58J35, 35K05
- Language
In this paper we prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply such estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature.
Comment: 39 pages. All comments are welcome. Theorem 1.4 and Section 7 added