3 citations · 13 across the 26 of their papers we have counts for
28 papers
Rigidity and weak notions of spectral scalar curvature
Xiaoxiang Chai
We give a weak formulation of spectral scalar curvature bounded from below via establishing a dihedral rigidity result. Given some special convex polyhedron, if another metric are…
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…
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…
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 lower…
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…
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…
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…
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…
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…
Spectral constant rigidity of warped product metrics
Xiaoxiang Chai, Juncheol Pyo, Xueyuan Wan
A theorem of Llarull says that if a smooth metric on the -sphere is bounded below by the standard round metric and the scalar curvature of is bounde…
A tilted spacetime positive mass theorem
Xiaoxiang Chai
We show a spacetime positive mass theorem for asymptotically flat initial data sets with a noncompact boundary. We develop a mass type invariant and a boundary dominant energy cond…
Scalar curvature comparison of rotationally symmetric sets
Xiaoxiang Chai, Gaoming Wang
Let be a compact 3-manifold with nonnegative scalar curvature . The boundary is diffeomorphic to the boundary of a rotationally symmetric and weakl…
Dihedral rigidity in hyperbolic 3-space
Xiaoxiang Chai, Gaoming Wang
We prove a comparison theorem for certain types of polyhedra in a 3-manifold with its scalar curvature bounded below by . The result confirms in some cases the Gromov dihedral…
The mass of an asymptotically hyperbolic end and distance estimates
Xiaoxiang Chai, Xueyuan Wan
Let be a complete connected -dimensional Riemannian spin manifold without boundary such that the scalar curvature satisfies and …
Band width estimates of CMC initial data sets
Xiaoxiang Chai, Xueyuan Wan
We generalize a band width estimate of Gromov to CMC initial data sets. We give three independent proofs: via the stability of a hypersurface with prescribed null expansion, via a…
A curvature estimate for stable marginally outer trapped hypersurface with a free boundary
Xiaoxiang Chai
A marginally outer trapped hypersurface is a generalization of minimal hypersurfaces originated from general relativity. We show a curvature estimate for stable marginally outer tr…
Inverse mean curvature flow with a free boundary in hyperbolic space
Xiaoxiang Chai
We study inverse mean curvature flow with free boundary supported on geodesic spheres in hyperbolic space. Starting from any convex hypersurface inside a geodesic ball with a free…
A perturbation of spacetime Laplacian equation
Xiaoxiang Chai
We study a perturbation \begin{equation} Δu + P | \nabla u| = h | \nabla u|, \end{equation} of spacetime Laplacian equation in an initial data set where is the trac…
Hypersurfaces of prescribed null expansion
Xiaoxiang Chai
We study hypersurfaces with prescribed null expansion in an initial data set. We propose a notion of stability and prove a topology theorem. Eichmair's Perron approach toward the e…
Scalar curvature, mean curvature and harmonic maps to the circle
Xiaoxiang Chai, Inkang Kim
We study harmonic maps from a 3-manifold with boundary to and prove a special case of dihedral rigidity of three dimensional cubes whose dihedral angles are .…
Mass and polyhedra in asymptotically hyperbolic manifolds
Xiaoxiang Chai
Using the upper half space model, we evaluate a component of the hyperbolic mass functional evaluated on a special family of polyhedra extending a formula of Miao-Piubello.
Asymptotically hyperbolic manifold with a horospherical boundary
Xiaoxiang Chai
We discuss asymptotically hyperbolic manifold with a noncompact boundary which is close to a horosphere in a certain sense. The model case is a horoball or the complement of a horo…
A note on Minkowski formula of conformal Killing-Yano -form
Xiaoxiang Chai
We study the Minkowski formula of conformal Killing-Yano two-forms in a spacetime of constant curvature. We establish the spacetime Alexandrov theorem with a free boundary.