4 papers
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…
Warped area-minimizing hypersurface and warped product metric
Yukai Sun
By studying the warped(or weighted) area-minimizing hypersurface, we prove that the metric can be locally split as a warped product metric under the spectral Ricci or spectral scal…
Gap phenomenon for scalar curvature
Yukai Sun, Changliang Wang
Inspired by Goette-Semmelmann \cite{GSSU2002}, we derive an estimate for the scalar curvature without a nonnegativity assumption on curvature operator. As an application, we show t…
Positive scalar curvature and isolated conical singularity
Xianzhe Dai, Yukai Sun, Changliang Wang
We prove a Geroch type result for isolated conical singularity. Namely, we show that there is no Riemannian metric on with an isolated conical singularity which ha…