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Isoperimetric inequalities and the gap between the first and second eigenvalues of an Euclidean domain

✍ Scribed by Shiu-Yuen Cheng; Kevin Oden

Book ID
105657629
Publisher
Springer-Verlag
Year
1997
Tongue
English
Weight
710 KB
Volume
7
Category
Article
ISSN
1050-6926

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✍ JosΓ© F Escobar πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 142 KB

Let (M n , g) be a compact Riemannian manifold with boundary. In this paper we give upper and lower estimates for the first nonzero Steklov eigenvalue where & 1 is a positive real number. The estimate from below is for a star-shaped domain on a manifold whose Ricci curvature is bounded from below.