Abstract
Let M be a closed Riemannian manifold with a family of Riemannian metrics $${g_{\it ij}(t)}$$gij(t) evolving by geometric flow (Formula Presnted) is a family of smooth symmetric two-tensors on M. In this paper we derive differential Harnack estimates for positive solutions to the nonlinear heat equation with potential: (Formula Presnted) ,where $${\gamma (t)}$$γ(t) is a continuous function on t, a is a constant and (Formula Presnted) is the trace of (Formula Presnted). Our Harnack estimates include many known results as special cases, and moreover lead to new Harnack inequalities for a variety geometric flows.
Original language | English |
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Pages (from-to) | 471-484 |
Number of pages | 14 |
Journal | manuscripta mathematica |
Volume | 148 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 2015 Nov 1 |
Externally published | Yes |
Keywords
- 53C21
- 53C44
ASJC Scopus subject areas
- Mathematics(all)