Math @ Duke
|
Publications [#361421] of Mark A. Stern
Papers Published
- Cerbo, LFD; Stern, M, Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence
(September, 2019)
(last updated on 2024/04/24)
Abstract: We study Betti numbers of sequences of Riemannian manifolds which
Benjamini-Schramm converge to their universal covers. Using the Price
inequalities we developed elsewhere, we derive two distinct convergence
results. First, under a negative Ricci curvature assumption and no assumption
on sign of the sectional curvature, we have a convergence result for weakly
uniform discrete sequences of closed Riemannian manifolds. In the negative
sectional curvature case, we are able to remove the weakly uniform discreteness
assumption. This is achieved by combining a refined Thick-Thin decomposition
together with a Moser iteration argument for harmonic forms on manifolds with
boundary.
|
|
dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
| |
Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
|
|