A maximum principle for $P$-harmonic maps with $L^q$ finite energy
HTML articles powered by AMS MathViewer
- by Kensho Takegoshi PDF
- Proc. Amer. Math. Soc. 126 (1998), 3749-3753 Request permission
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
- Shiu Yuen Cheng, Liouville theorem for harmonic maps, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 147–151. MR 573431
- S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), no. 3, 333–354. MR 385749, DOI 10.1002/cpa.3160280303
- J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), no. 1, 1–68. MR 495450, DOI 10.1112/blms/10.1.1
- Samuel I. Goldberg and Zvi Har’El, A general Schwarz lemma for Riemannian-manifolds, Bull. Soc. Math. Grèce (N.S.) 18 (1977), no. 1, 141–148. MR 528427
- Peter Li and Richard Schoen, $L^p$ and mean value properties of subharmonic functions on Riemannian manifolds, Acta Math. 153 (1984), no. 3-4, 279–301. MR 766266, DOI 10.1007/BF02392380
- Nakauchi,N., A Liouville type theorem for $p$-harmonic maps, preprint.
- Richard Schoen and Shing Tung Yau, Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature, Comment. Math. Helv. 51 (1976), no. 3, 333–341. MR 438388, DOI 10.1007/BF02568161
- Chun Li Shen, A generalization of the Schwarz-Ahlfors lemma to the theory of harmonic maps, J. Reine Angew. Math. 348 (1984), 23–33. MR 733920, DOI 10.1515/crll.1984.348.23
- Takegoshi,K., A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds, to appear in Nagoya Mathematical Journal.
- Shing Tung Yau, Some function-theoretic properties of complete Riemannian manifold and their applications to geometry, Indiana Univ. Math. J. 25 (1976), no. 7, 659–670. MR 417452, DOI 10.1512/iumj.1976.25.25051
- Shing Tung Yau, A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978), no. 1, 197–203. MR 486659, DOI 10.2307/2373880
Additional Information
- Kensho Takegoshi
- Affiliation: Department of Mathematics, Graduate School of Science, Machikaneyama-cho 1-16, Toyonaka-shi Osaka, 560 Japan
- Email: kensho@math.wani.osaka-u.ac.jp
- Received by editor(s): April 21, 1997
- Communicated by: Peter Li
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3749-3753
- MSC (1991): Primary 58D15, 58E20
- DOI: https://doi.org/10.1090/S0002-9939-98-04609-7
- MathSciNet review: 1469437