1UNIVERSITY OF SUSSEX, BRIGHTON, BN1 9QH, UK.
|刊名：||International Journal of Analysis and Applications, 2014, Vol.6 (1)|
|原始语种摘要：||In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.|