The seminar usually takes place in 515, Cosmology Building at 4-5PM every Wednesday, unless noted otherwise.
Organizers: Siao-Hao Guo 郭孝豪 (NTU), Chao-Ming Lin 林朝明 (NTU), Wei-Bo Su 蘇瑋栢 (NCU), Chung-Jun Tsai 蔡忠潤 (NTU)
Kai-Wei Zhao 趙凱衞 (University of California, Riverside): Obata-type rigidity on static manifolds with boundary
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.
Guoran Ye 叶果然 (Northwestern University): Special Lagrangians with Cylindrical Tangent Cones
We construct special Lagrangian submanifolds $Y\subset \C^{n+1},n\geq 3$ in a neighborhood of the origin, with an isolated singularity, but with cylindrical tangent cone $C\times\R$. Such examples exist, for example, when $C$ is a pair of transverse planes. The construction glues exact Lagrangian graphs. While the construction is purely analytic, it is important to recognize that the leading term of the Lagrangian potential in the gluing region exhibits cohomological information.
Yi-Lin Tsai 蔡宜霖 (NCTS)
The Second Workshop on Geometric Variational Problems, Geometric Measure Theory, and Related Topics
Junyoung Park 박 준영 (Rutgers)
