Journal article

### Sharp Cheeger–Buser type inequalities in RCD(K,∞) spaces

Abstract:

The goal of the paper is to sharpen and generalise bounds involving Cheeger’s isoperimetric constant h and the first eigenvalue λ1 of the Laplacian. A celebrated lower bound of λ1 in terms of h, λ1≥h2/4, was proved by Cheeger in 1970 for smooth Riemannian manifolds. An upper bound on λ1 in terms of h was established by Buser in 1982 (with dimensional constants) and improved (to a dimension-free estimate) by Ledoux in 2004 for smooth Riemannian manifolds with Ricci curvature bounded below. The...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Version of record, 427.6KB)
Publisher copy:
10.1007/s12220-020-00358-6

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hilda's College
Role:
Author
ORCID:
0000-0002-1932-7148
Publisher:
Springer Verlag Publisher's website
Journal:
Journal of Geometric Analysis Journal website
Volume:
31
Pages:
2416–2438
Publication date:
2020-02-14
Acceptance date:
2020-01-12
DOI:
EISSN:
1559-002X
ISSN:
1050-6926
Source identifiers:
1061625
Language:
English
Keywords:
Pubs id:
pubs:1061625
UUID:
uuid:1f9e6684-a046-4616-97ed-641e6d25c236
Local pid:
pubs:1061625
Deposit date:
2019-10-11