6 papers
Compact locally conformal Kähler manifolds with constant Chern holomorphic sectional curvature
Zhuzhu Huang, Xueyuan Wan
We prove the Chern version of the constant holomorphic sectional curvature conjecture for compact locally conformal Kähler manifolds. More precisely, let , , be a…
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…
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…
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…