Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A maximum principle for $P$-harmonic maps
with $L^{q}$ finite energy

Author: Kensho Takegoshi
Journal: Proc. Amer. Math. Soc. 126 (1998), 3749-3753
MSC (1991): Primary 58D15, 58E20
MathSciNet review: 1469437
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show a maximum principle for $P$-harmonic maps with $L^q$-finite energy. As an application we can generalize a non-existence theorem for harmonic maps with finite Dirichlet integral by Schoen and Yau to those maps.

References [Enhancements On Off] (What's this?)

  • [C] Cheng,S.Y., Liouville theorem for harmonic maps, Proceedings of Symposia in Pure Mathematics 36 (1980), 147-151. MR 81i:58021
  • [C-Y] Cheng,S.Y., Yau,S.T., Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333-354. MR 52:6608
  • [E-L] Eells,J., Lemaire,L., A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1-68. MR 82b:58033
  • [G-H] Goldberg,S.I., Har'el,Z., A general Schwarz lemma for Riemannian manifolds, Bull. Soc. Math. Grèce 18 (1977), 141-148. MR 80c:53055
  • [L-S] Li,P., Schoen,R., $L^{p}$ and mean value properties of subharmonic functions on Riemannian manifolds, Acta Math. 153 (1984), 279-301. MR 86j:58147
  • [N] Nakauchi,N., A Liouville type theorem for $p$-harmonic maps, preprint.
  • [Sc-Y] Schoen,R., Yau,S.T., Harmonic maps and the topology of stable hypersurfaces and manifolds of nonnegative Ricci curvature, Comment. Math. Helv. 51 (1976), 333-341. MR 55:11302
  • [Sh] Shen,C-L., A generalization of the Schwarz-Ahlfors lemma to the theory of harmonic maps, J. Reine Angew. Math. 348 (1984), 23-33. MR 85i:58044
  • [T] Takegoshi,K., A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds, to appear in Nagoya Mathematical Journal.
  • [Y-1] Yau,S.T., Some function theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J. 25 (1976), 656-670. MR 54:5502
  • [Y-2] Yau,S.T., A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978), 197-203. MR 58:6370

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58D15, 58E20

Retrieve articles in all journals with MSC (1991): 58D15, 58E20

Additional Information

Kensho Takegoshi
Affiliation: Department of Mathematics, Graduate School of Science, Machikaneyama-cho 1-16, Toyonaka-shi Osaka, 560 Japan

Received by editor(s): April 21, 1997
Communicated by: Peter Li
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society