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UPA Perpustakaan Universitas Jember

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

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By Cheeger’s isoperimetric constants, some lower bounds and upper bounds of λ1,
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)

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