Abstract: 

Inverse curvature type flows have long been recognized for their use in deriving various geometric inequalities, such as the Riemannian Penrose inequality, isoperimetric-type inequalities, and Alexandrov-Fenchel inequalities. Most of these results are comparison theorems of two geometric quantities, though there are a few exceptions. In this talk, I will present two families of weighted geometric inequalities that involve three geometric quantities for hypersurfaces in some warped product manifolds. A main ingredient is identifying monotone quantities involving two quantities along the flow. This is joint work in progress with Yong Wei.