Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds

03/28/2023 12:00 pm - 1:00 pm
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Member Seminar

Speaker: Jue Liu

Title: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds

Abstract: The study of quasilocal mass in general relativity has a long history. In previous papers by many authors we have a deep understanding of the properties of quasilocal mass such as positivity, rigidity and asymptotics etc. In this talk I will focus on the monotonicity of quasilocal mass, which means the quasilocal mass of a finite region is smaller than that of a larger region containing the previous region. Motivated by the definition of Bartnik mass and Brown-York mass, we define a new quasilocal mass using the Hamilton method. With this definition, we derive the sufficient condition such that the quasilocal mass is monotonic. As an application I will also discuss the relationship with the Bartnik conjecture, that is under what conditions there will be a static extension to the given Bartnik data.