25 jun 2025 -- 16:00   [open in google calendar]

Scuola Normale Superiore, Aula Bianchi Scienze

Abstract.

In this talk, we will introduce general monotone quantities and geometric inequalities associated with $p$-capacitary functions in asymptotically flat $3$-manifolds with simple topology and nonnegative scalar curvature. The inequalities become equalities on the spatial Schwarzschild manifolds outside rotationally symmetric spheres. This generalizes Miao’s result from $p = 2$ to $1 < p < 3$. Then we want to talk about some applications, including mass-to-$p$-capacity and $p$-capacity-to-area inequalities due to Bray-Miao and Xiao. This is a joint work with Professor Chao Xia and Professor Jiabin Yin.