A new result on the pinching of the first eigenvalue of the Laplacian and the Dirichlet diameter conjecture (Q1313325)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A new result on the pinching of the first eigenvalue of the Laplacian and the Dirichlet diameter conjecture |
scientific article; zbMATH DE number 490696
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new result on the pinching of the first eigenvalue of the Laplacian and the Dirichlet diameter conjecture |
scientific article; zbMATH DE number 490696 |
Statements
A new result on the pinching of the first eigenvalue of the Laplacian and the Dirichlet diameter conjecture (English)
0 references
13 March 1994
0 references
We prove that a Riemannian \(n\)-manifold with Ricci curvature \(\geq(n-1)\) and sectional curvature bounded from above, is a sphere provided the first eigenvalue of its Laplacian (resp. its diameter) is sufficiently close to \(n\) (resp. to \(\pi\)).
0 references
pinching condition
0 references
Ricci curvature
0 references
sectional curvature
0 references
first eigenvalue
0 references
Laplacian
0 references
diameter
0 references
0 references
