Eigenvalues and Capacities of Riemannian Manifolds
نویسندگان
چکیده
This paper is concerned with eigenvalues of the biharmonic operators and the buckling eigenvalue for complete Riemannian manifolds. We are mostly concerned with relating bounds for these eigenvalues to the behavior of the ends of the manifold. Let M be a complete Riemannian manifold. M is called parabolic if every non-positive subharmonic function on M reduces to a constant. By an end E of M we mean an unbounded connected component of the complement of a compact subset. An end E will be called parabolic if there exists a complete parabolic Riemannian manifold whose only end is E .If M is a surface these concepts are conformally invariant. Let Ω ⊂⊂ M be a relatively compact subdomain with smooth boundary. Let P > 0 be a smooth function on M and consider the eigenvalue problem
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