L-p harmonic 1-forms on minimal hypersurfaces with finite index

초록

Let N be a complete simply connected Riemannian manifold with sectional curvature K-N satisfying -k(2) <= K-N <= 0 for a nonzero constant k. In this paper we prove that if M is an n(>= 3)-dimensional complete minimal hypersurface with finite index in N, then the space of L-p harmonic 1-forms on M must be finite dimensional for certain p > 0 provided the bottom of the spectrum of the Laplace operator is sufficiently large. In particular, M has finitely many ends. These results can be regarded as an extension of Li-Wang (2002). (c) 2018 Elsevier B.V. All rights reserved.

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