Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 3: 583 - 594

DOI: https://doi.org/10.1007/s11464-015-0422-x

RESEARCH ARTICLE

Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds

  • Feng DU 1 ,
  • Jing MAO , 2
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  • 1. School of Mathematics and Physics Science, Jingchu University of Technology, Jingmen 448000, China
  • 2. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

Received date: 14 Nov 2013

Accepted date: 22 Jul 2014

Published date: 01 Apr 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

For a compact Riemannian manifold M immersed into a higher dimensional manifold which can be chosen to be a Euclidean space, a unit sphere, or even a projective space, we successfully give several upper bounds in terms of the norm of the mean curvature vector of M for the first non-zero eigenvalue of the p-Laplacian (1<p<+∞) on M. This result can be seen as an extension of Reilly’s bound for the first non-zero closed eigenvalue of the Laplace operator.

Key words： p-Laplacian; eigenvalue; mean curvature vector

Cite this article

Feng DU , Jing MAO . Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds[J]. Frontiers of Mathematics in China, 2015 , 10(3) : 583 -594 . DOI: 10.1007/s11464-015-0422-x

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