题目：On some Integral and Pointwise Monotonicity Formulae in the Curvature Flows
报告人：郭洪欣 教授 （温州大学）
摘要：Monotonicity formulae are fundamental in the studies of long term behavior of geometric flows. For a wide class of monotonicity formulae, there is a strategy to define them as follows. Calculate the first two derivatives of the Boltzmann entropy of positive solutions to the heat type equations associated to the flow, and then modify the quantities to fit shrinking or expanding self-similar solutions. Calculate pointwisely one gets the corresponding Harnack inequalities. In this talk, we first review Perelman's entropy and its pointwise version for the Ricci flow and then we discuss monotonicity formulae for the Gaussian curvature flow and the curve shortening flow.
All are welcome!