Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Degenerating hyperbolic surfaces and spectral gaps for large genus

Yunhui Wu, Haohao Zhang and Xuwen Zhu

Vol. 17 (2024), No. 4, 1377–1395
Abstract

We study the differences of two consecutive eigenvalues λi λi1, i up to 2g 2, for the Laplacian on hyperbolic surfaces of genus g, and show that the supremum of such spectral gaps over the moduli space has infimum limit at least 1 4 as the genus goes to infinity. A min-max principle for eigenvalues on degenerating hyperbolic surfaces is also established.

Keywords
spectral gaps, min-max principle, large genus
Mathematical Subject Classification
Primary: 32G15
Secondary: 58C40
Milestones
Received: 25 January 2022
Revised: 29 July 2022
Accepted: 23 September 2022
Published: 17 May 2024
Authors
Yunhui Wu
Yau Mathematical Sciences Center
Tsinghua University
Beijing
China
Haohao Zhang
Tsinghua University
Beijing
China
Xuwen Zhu
Department of Mathematics
Northeastern University
Boston, MA
United States

Open Access made possible by participating institutions via Subscribe to Open.