Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T16:16:44.316Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on p-Harmonic 1-Forms on Complete Manifolds

Published online by Cambridge University Press:  20 November 2018

Xi Zhang
Xi Zhang*
Affiliation:
Department of Mathematics West Brook Campus Zhejiang University Hangzhou 310028 People’s Republic of China, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we prove that there is no nontrivial ${{L}^{q}}$-integrably $p$-harmonic 1-form on a complete manifold with nonnegatively Ricci curvature $\left( 0\,<\,q\,<\,\infty \right)$.

Keywords

58E2053C21p-harmonic1-formcomplete manifoldSobolev inequality
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 3 , 01 September 2001 , pp. 376 - 384
Copyright
Copyright © Canadian Mathematical Society 2001

References

[1] Greene, R. and Wu, H., Harmonic forms on noncompact Riemannian and Kähler manifolds. Michigan.Math. J. 28 (1981), 63–81.Google Scholar
[2] Saloff-Coste, L., Uniformly elliptic operators on Riemannian manifolds. J. Differential Geom. 36 (1992), 417–450.Google Scholar
[3] Moser, J., On Harnack's theorem for elliptic equations. Comm. Pure Appl. Math. 14 (1961), 577–591.Google Scholar
[4] Li, P., Lecture Notes on Geometric Analysis. Lecture Notes Series 6, Research Institute of Mathematics and Global Analysis Research Center, Seoul National University. Seoul, 1993.Google Scholar
[5] Schoen, R. and Yau, S. T., Harmonic Maps and the Topology of Stable Hypersurfaces and manifolds with nonnegative Ricci curvature. Comment.Math. Helv. 39 (1976), 333–341.Google Scholar
[6] Yau, S. T., Some function-theoretic properties of complete Riemannian manifolds and the applications to geometry. Indiana Math. J. 25 (1976), 659–679.Google Scholar
[7] Calabi, E., On manifolds with nonnegative Ricci curvature. Notices Amer.Math. Soc. 22(1975), A205.Google Scholar
[8] Eells, J. and Lemaire, L., Selected Topics in Harmonic Maps. CBMS Regional Conf. Series 50, Amer. Math. Soc, 1983.Google Scholar