6 papers
Bottom spectrum, vertical -cowaist and scalar curvature rigidity
Daoqiang Liu
We introduce the vertical \(\widehat{A}\)-cowaist, a codimension-one invariant for partitioned manifolds. It extends the concept of infinite vertical \(\widehat{A}\)-cowaist for ba…
A sharp inequality relating scalar curvature, bottom spectrum, and the relative -cowaist on complete manifolds
Daoqiang Liu
We introduce a refined notion of relative -cowaist, extending the framework of Cecchini--Zeidler to complete manifolds, which may be noncompact and have compact bounda…
Bottom spectrum and Llarull's theorem on complete noncompact manifolds
Daoqiang Liu
In this paper, we prove an extension of the noncompact version of Llarull's theorem due to Zhang and Li-Su-Wang-Zhang, giving an upper bound for the infimum of scalar curvature in…
Llarull's theorem on noncompact manifolds with boundary
Bo Liu, Daoqiang Liu
Recently, Zhang \cite{Zh20} and Li-Su-Wang-Zhang \cite{LSWZ24+} generalized Llarull's theorem to the noncompact complete spin manifold. In this paper, we further extend their resul…
Complexity factor for a static self-gravitating sphere in Rastall-Rainbow gravity
Zhou-Li Ye, Yu Wang, Rui-Xin Yang +1
We generalized Herrera's definition of complexity factor for static spherically symmetric fluid distributions to Rastall-Rainbow theory of gravity. For this purpose, an energy-depe…
On distance estimates for complete manifolds with lower scalar curvature bounds
Daoqiang Liu
In this paper, we focus on the distance estimate problem on complete manifolds with compact boundary and with lower scalar curvature bounds. On these manifolds, relative to a backg…