Notices of the International Consortium of Chinese Mathematicians

Volume 6 (2018)

Number 2

Small eigenvalues of surfaces: old and new

Pages: 9 – 24

DOI: https://dx.doi.org/10.4310/ICCM.2018.v6.n2.a3

Authors

Werner Ballmann (Max Planck Institute for Mathematics, Bonn and Hausdorff Center for Mathematics, Bonn, Germany)

Henrik Matthiesen (Max Planck Institute for Mathematics, Bonn and Hausdorff Center for Mathematics, Bonn, Germany)

Sugata Mondal (Indiana University, Bloomington, Indiana, U.S.A.)

Abstract

We discuss our recent work on small eigenvalues of surfaces. As an introduction, we present and extend some of the by now classical work of Buser and Randol and explain novel ideas from articles of Sévennec, Otal, and Otal–Rosas which are of importance in our line of thought.

Keywords

Laplace operator, small eigenvalue, analytic systole

2010 Mathematics Subject Classification

35P15, 53C99, 58J50

Full Text (PDF format)

We would like to thank Bram Petri and Federica Fanoni for pointing out the results of [20] to us. We would also like to thank the referee for useful comments. We are grateful to the Max Planck Institute for Mathematics, the Hausdorff Center for Mathematics, and Indiana University at Bloomington for their support and hospitality.

Published 16 May 2019