# Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature

Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature By Cheeger’s isoperimetric constants, some lower bounds and upper bounds of λ 1 $\lambda_{1}$ , the first eigenvalue on a complete surface of constant curvature, are given. Some Bonnesen-style inequalities and reverse Bonnesen-style inequalities for the first eigenvalue are obtained. Those Bonnesen-style inequalities obtained are stronger than the well-known Osserman’s results and the upper bound is stronger than Osserman’s results (Osserman in Proceedings of the International Congress of Mathematicians, Helsinki, 1978). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inequalities and Applications Springer Journals

# Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature

, Volume 2017 (1) – Aug 15, 2017
11 pages

/lp/springer-journals/bonnesen-style-inequality-for-the-first-eigenvalue-on-a-complete-t0mrn3BTdQ
Publisher
Springer Journals
Subject
Mathematics; Analysis; Applications of Mathematics; Mathematics, general
eISSN
1029-242X
D.O.I.
10.1186/s13660-017-1462-4
Publisher site
See Article on Publisher Site

### Abstract

By Cheeger’s isoperimetric constants, some lower bounds and upper bounds of λ 1 $\lambda_{1}$ , the first eigenvalue on a complete surface of constant curvature, are given. Some Bonnesen-style inequalities and reverse Bonnesen-style inequalities for the first eigenvalue are obtained. Those Bonnesen-style inequalities obtained are stronger than the well-known Osserman’s results and the upper bound is stronger than Osserman’s results (Osserman in Proceedings of the International Congress of Mathematicians, Helsinki, 1978).

### Journal

Journal of Inequalities and ApplicationsSpringer Journals

Published: Aug 15, 2017

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