L-P p-harmonic 1-forms on submanifolds in a Hadamard manifold

摘要

Let M-m(m >= 3) be an m-dimensional complete noncompact oriented submanifold with finite total curvature, in a Hadamard manifold Nm+n with the sectional curvature satisfying -k(2) < K-N <= 0, where k is a positive constant. If there exists point q is an element of M such that K-N(q) not equal 0, assume further that the first eigenvalue of the Laplace-Beltrami operator of M is bounded by a suitable constant. We obtain that the dimension of H-1,H-p(M) is finite, that is, dimH(1,p)(M) < infinity. (C) 2016 Elsevier B.V. All rights reserved.