arXiv subjects
Publications and source records attributed to Chengzhang Sun.
Through a careful analysis of the Yamabe equation on singular spaces, we establish a positive mass theorem for singular asymptotically hyperbolic manifolds with arbitrary ends. We also derive a rigidity result that is novel even in the smooth setting.
For a parabolically convex domain $M\subseteq \mathbb{H}^n$, $n\ge 3$, we prove that if $f:(N,\bar g)\to (M,g)$ has nonzero degree, where $N$ is spin with scalar curvature $R_N\ge -n(n-1)$, and if $f|_{\partial N}$ does not increase the distance and the mean curvature, then $N$ is hyperbolic, and $\partial N$ is isometric to $\partial M$. This is a partial generalization of Lott's result \cite{lott2021index} to negative lower bounds of scalar curvature.
The paper studies the $L^2$-torsion of fibrations, focusing on cases that relax acyclicity and the determinant class condition. We prove the sum formula and the product formula for $L^2$-torsion in the extended abelian category. The desired formula for $L^2$-torsion of a simple fibration is obtained under the assumption that the fibers have zero Euler characteristic.