标题： 曲面上Ricci流沿Liouville熵的单调性 显示英文标题

标题： Monotonicity of the Liouville entropy along the Ricci flow on surfaces

摘要： 利用几何和微观局部方法，我们证明了非常数负曲率的闭曲面上测地流的刘维尔熵在归一化里奇流下是严格增加的。 这正面回答了曼宁在2004年提出的问题。 更一般地，在这种情况下，我们得到了刘维尔熵沿任意保面积保形扰动导数的一个显式公式。 此外，我们还证明了平均根曲率——一个纯几何量，且是刘维尔熵的一个下界——在归一化里奇流下也是严格增加的。 显示英文摘要

摘要： Using geometric and microlocal methods, we show that the Liouville entropy of the geodesic flow of a closed surface of non-constant negative curvature is strictly increasing along the normalized Ricci flow. This affirmatively answers a question of Manning from 2004. More generally, we obtain an explicit formula for the derivative of the Liouville entropy along arbitrary area-preserving conformal perturbations in this setting. In addition, we show the mean root curvature, a purely geometric quantity which is a lower bound for the Liouville entropy, is also strictly increasing along the normalized Ricci flow.