p-Harmonic functions and connectedness at infinity of complete submanifolds in a Riemannian manifold
- Authors
- Dung, Nguyen Thac; Seo, Keomkyo
- Issue Date
- Aug-2017
- Publisher
- SPRINGER HEIDELBERG
- Keywords
- p-Harmonic function; p-Nonparabolicity; delta-Stability; The first eigenvalue; Connectedness at infinity
- Citation
- ANNALI DI MATEMATICA PURA ED APPLICATA, v.196, no.4, pp 1489 - 1511
- Pages
- 23
- Journal Title
- ANNALI DI MATEMATICA PURA ED APPLICATA
- Volume
- 196
- Number
- 4
- Start Page
- 1489
- End Page
- 1511
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/8210
- DOI
- 10.1007/s10231-016-0625-0
- ISSN
- 0373-3114
1618-1891
- Abstract
- In this paper, we study the connectedness at infinity of complete submanifolds by using the theory of p-harmonic function. For lower-dimensional cases, we prove that if M is a complete orientable noncompact hypersurface in Rn+1 and if delta-stability inequality holds on M, then M has only one p-nonparabolic end. It is also proved that if M-n is a complete noncompact submanifold in R-n vertical bar k with sufficiently small L-n norm of the traceless second fundamental form, then M has only one p-nonparabolic end. Moreover, we obtain a lower bound of the fundamental tone of the p Laplace operator on complete submanifolds in a Riemannian manifold.
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