Recognition: unknown
Some rigidity theorems for spectral curvature bounds
read the original abstract
We investigate the geometric implications of spectral curvature bounds, extending classical rigidity results in scalar curvature geometry to the spectral setting. By systematically employing the warped $\mu$-bubble method, we show classification theorems for stable weighted minimal hypersurfaces in 3-manifolds with nonnegative spectral scalar curvature, and we establish band width estimates for both spectral Ricci and spectral scalar curvatures. Furthermore, we prove some splitting theorems under spectral curvature conditions, including a spectral version of the Geroch conjecture for manifolds with arbitrary ends and a result related to the Milnor conjecture.
This paper has not been read by Pith yet.
Forward citations
Cited by 2 Pith papers
-
Rigidity and flexibility under spectral Ricci lower bounds and mean-convex boundary
Under spectral Ricci bounds and mean-convex boundary, complete manifolds split isometrically as products or admit positive sectional curvature metrics in dimensions other than 4.
-
Intermediate curvature and splitting theorem
Rigidity theorems establish that nonnegative m-intermediate curvature forces product splitting with Euclidean space in dimensions 3-7 for restricted m, with constructions proving the condition m² - mn + m + n > 0 is sharp.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.