Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T01:29:31.808Z Has data issue: false hasContentIssue false
  • English
  • Français

On $p$-harmonic morphisms and conformally flat spaces

Published online by Cambridge University Press:  05 September 2005

YE-LIN OU
YE-LIN OU
Affiliation:
Department of Mathematics, University of Oklahoma, Norman, OK 73019, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a method to construct non-trivial $p$-harmonic morphisms via conformal change of the metric on the domain and/or the target manifold (Theorems 2.1, 2.5 and 2.8). As applications, we show the existence of higher dimensional harmonic spheres in general manifolds (Theorem 2.10) generalizing Sacks and Uhlenbeck's result on harmonic 2-spheres, prove some existence theorems for non-trivial $p$-harmonic morphisms between conformally flat spaces (Theorems 2.12, 3.1 and 3.2), give a method to construct minimal foliations via $p$-harmonic morphisms and show that many $\mathbf{R}^{m}$ with a conformally flat metric admit minimal foliations of codimension greater than two (Theorems 3.3, 3.4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 139 , Issue 2 , September 2005 , pp. 317 - 332
Copyright
2005 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)