J Austral Math Soc Ser A 50 pp409--416, 1991.

On the Consecutive Eigenvalues of the Laplacian of a Compact Minimal Submanifold in a Sphere

Pui-Fai Leung

Abstract

Let 0 = l₀ < l₁ £ l₂ £ l₃ £ ... denote the sequence of eigenvalues of the Laplacian of a compact minimal submanifold in a unit sphere. Yang and Yau obtained an upper bound on l_n+1 in terms of l_n and the sum l₁ + ... + l_n. In this note we shall prove an improved version of this upper bound by using the method of Hile and Protter.

1980 AMS Subject Classification (1985 Revision): 53C40, 35P15

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Authors

Pui-Fai Leung

National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511.