REVIEW 2 cited by
A sharp spectral splitting theorem
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We prove a sharp spectral generalization of the Cheeger--Gromoll splitting theorem. We show that if a complete non-compact Riemannian manifold $M$ of dimension $n\geq 2$ has at least two ends and \[ \lambda_1(-\gamma\Delta+\mathrm{Ric})\geq 0, \] for some $\gamma<\frac{4}{n-1}$, then $M$ splits isometrically as $\mathbb R\times N$ for some compact manifold $N$ with nonnegative Ricci curvature. We show that the constant $\frac{4}{n-1}$ is sharp, and the multiple-end assumption is necessary for any $\gamma>0$.
Forward citations
Cited by 2 Pith papers
-
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound
Complete 3-manifolds with scalar curvature lower bound, finitely many ends, and finite first Betti number satisfy a sharp bottom spectrum upper bound and are parabolic under positive scalar curvature.
-
Some rigidity theorems for spectral curvature bounds
Spectral lower bounds on scalar/Ricci curvature imply the same rigidity, band-width, and splitting conclusions as classical pointwise bounds, via warped µ-bubbles.
Discussion (0). Sign in to comment.