5 papers · 1 filter
Spectral Geroch conjecture and noncompact area enlargeable summands
Daoqiang Liu
We prove that the connected sum of a possibly noncompact area enlargeable manifold with an arbitrary spin manifold of the same dimension admits no complete Riemannian m…
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…