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math.DG2024
Initial data set rigidity results for polyhedra
Xiaoxiang Chai, Xueyuan Wan
Using spinors, we show a dihedral type rigidity for polyhedral initial data sets. This rigidity connects spacetime positive mass theorem, dihedral rigidity and capillary marginally…
math.DG2024
Scalar curvature rigidity of domains in a warped product
Xiaoxiang Chai, Xueyuan Wan
By exploiting the conformality of a warped product metric with a direct product metric, we develop a new connection on a twisted spinor bundle and its associated Dirac operator. We…
math.DG2024
A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Plane
Xiaoxiang Chai, Yimin Chen
We prove a new Minkowski type formula for capillary hypersurfaces supported on totally geodesic hyperplanes in hyperbolic space. It leads to a volume-preserving flow starting from…