Abstract

Static manifolds naturally arise in general relativity and as obstructions to deformation of scalar curvature. In this talk, we will study rigidity and deformability properties of b-static metrics on simple manifolds with compact boundary, imposing a Robin-type boundary condition on static potentials, associated with the coupled map of scalar curvature and boundary mean curvature. By establishing a spectral correspondence between the induced boundary static operator and the stability operator of marginally outer trapped surfaces (MOTS), we show that boundary stability enforces global positivity of b-static potentials, thereby excluding the existence of interior horizons. Building on this spectral framework, we obtain an Obata-type rigidity classification by using an integral identity. We further derive sufficient geometric conditions ensuring the local surjectivity of the coupled curvature map. This talk is based on joint work with Hongyi Sheng.

Zoom Link

https://us02web.zoom.us/j/84420826051?pwd=m6Ur6NXFKBQrDSvP1jjozDf5yum43S.1

Organizers

Siao-Hao Guo (NTU), Chao-Ming Lin (NTU), Wei-Bo Su (NCU), Chung-Jun Tsai (NTU)