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

Authors
Choi, HagyunSeo, Keomkyo
Issue Date
Jul-2018
Publisher
ELSEVIER SCIENCE BV
Keywords
L-p harmonic form; Minimal hypersurface; Finite index
Citation
JOURNAL OF GEOMETRY AND PHYSICS, v.129, pp 125 - 132
Pages
8
Journal Title
JOURNAL OF GEOMETRY AND PHYSICS
Volume
129
Start Page
125
End Page
132
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/4428
DOI
10.1016/j.geomphys.2018.03.006
ISSN
0393-0440
1879-1662
Abstract
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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