Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points
Publication
, Journal Article
Cerbo, LFD; Stern, M
Published in: Communications in Analysis and Geometry
November 29, 2022
We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly well for manifolds of non-positive sectional curvature, and in this case we prove a strengthened Price inequality. We employ these inequalities to study the asymptotic behavior of the Betti numbers of coverings of Riemannian manifolds without conjugate points. Finally, we give a vanishing result for $L^{2}$-Betti numbers of closed manifolds without conjugate points.
Duke Scholars
Published In
Communications in Analysis and Geometry
ISSN
1019-8385
Publication Date
November 29, 2022
Volume
30
Issue
2
Start / End Page
297 / 334
Publisher
International Press
Related Subject Headings
- Nuclear & Particles Physics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Cerbo, L. F. D., & Stern, M. (2022). Price Inequalities and Betti Number Growth on Manifolds without
Conjugate Points. Communications in Analysis and Geometry, 30(2), 297–334.
Cerbo, Luca F Di, and Mark Stern. “Price Inequalities and Betti Number Growth on Manifolds without
Conjugate Points.” Communications in Analysis and Geometry 30, no. 2 (November 29, 2022): 297–334.
Cerbo LFD, Stern M. Price Inequalities and Betti Number Growth on Manifolds without
Conjugate Points. Communications in Analysis and Geometry. 2022 Nov 29;30(2):297–334.
Cerbo, Luca F. Di, and Mark Stern. “Price Inequalities and Betti Number Growth on Manifolds without
Conjugate Points.” Communications in Analysis and Geometry, vol. 30, no. 2, International Press, Nov. 2022, pp. 297–334.
Cerbo LFD, Stern M. Price Inequalities and Betti Number Growth on Manifolds without
Conjugate Points. Communications in Analysis and Geometry. International Press; 2022 Nov 29;30(2):297–334.
Published In
Communications in Analysis and Geometry
ISSN
1019-8385
Publication Date
November 29, 2022
Volume
30
Issue
2
Start / End Page
297 / 334
Publisher
International Press
Related Subject Headings
- Nuclear & Particles Physics
- 4904 Pure mathematics
- 0101 Pure Mathematics