7 papers
Spectral Positive Mass Theorem for Asymptotically Hyperbolic 3-manifolds with Toroidal Infinity
Xiaoxiang Chai, Yimin Chen, Juncheol Pyo
We define a mass invariant adapted to the spectral scalar curvature for asymptotically hyperbolic 3-manifolds with toroidal infinity and show its positivity under a lower bound on…
Band width estimates with lower spectral curvature bounds
Xiaoxiang Chai, Yukai Sun
In this work, we use the warped \( μ\)-bubble method to study the consequences of a spectral curvature bound. In particular, with a lower spectral Ricci curvature bound and a lowe…
Some rigidity theorems for spectral curvature bounds
Xiaoxiang Chai, Yukai Sun
We investigate the geometric implications of spectral curvature bounds, extending classical rigidity results in scalar curvature geometry to the spectral setting. By systematically…
Llarull type theorems for bands in Three and Four dimensions
Xiaoxiang Chai, Xueyuan Wan
Llarull's theorem asserts that the scalar curvature and the metric on the -sphere cannot be bounded below at the same time by those of the standard -sphere. Using the warped…
Scalar curvature rigidity of domains in a 3-dimensional warped product
Xiaoxiang Chai, Gaoming Wang
A warped product with a spherical factor and a logarithmically concave warping function satisfies a scalar curvature rigidity of the Llarull type. We develop a scalar curvature rig…
Scalar curvature rigidity of parabolic convex polytopes in hyperbolic space
Xiaoxiang Chai, Xueyuan Wan
In odd dimensions, we prove a scalar curvature rigidity for parabolic convex polytopes in hyperbolic space enclosed by linear planes in the Poincare upper half-space model and conv…