Tohoku Mathematical Journal
2003
December
SECOND SERIES VOL. 55, NO. 4

Tohoku Math. J.
55 (2003), 529-541

Title BIHARMONIC CAPACITY AND THE STABILITY OF MINIMAL LAGRANGIAN SUBMANIFOLDS

Author Bennett Palmer

(Received November 5, 2001, revised November 18, 2002)
Abstract. We study the eigenvalues of the biharmonic operators and the buckling eigenvalue on complete, open Riemannian manifolds. We show that the first eigenvalue of the biharmonic operator on a complete, parabolic Riemannian manifold is zero. We give a generalization of the buckling eigenvalue and give applications to studying the stability of minimal Lagrangian submanifolds in Kahler manifolds.

2000 Mathematics Subject Classification. Primary 53A10; Secondary 35P15, 58E12.

Key words and phrases. Minimal Lagrangian submanifold, buckling eigenvalue.

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