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)

 
 

 

Harmonic maps with noncontact boundary values


Author: Harold Donnelly
Journal: Proc. Amer. Math. Soc. 127 (1999), 1231-1241
MSC (1991): Primary 58E20
DOI: https://doi.org/10.1090/S0002-9939-99-04627-4
MathSciNet review: 1473662
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Every rank one symmetric space $M$, of noncompact type, admits a compactification $\overline M$ by attaching a sphere $S^{n-1}$ at infinity. If $M$ does not have constant sectional curvature, then $\overline M-M$ admits a natural contact structure. This paper presents a number of harmonic maps $h$, from $M$ to $M$, which extend continuously to $\overline M$, and have noncontact boundary values. If the boundary values are assumed continuously differentiable, then the contact structure must be preserved.


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

  • 1. P. Bailey, L. Shampine, and P. Waltman, Nonlinear two point boundary value problems, Academic Press, NY and London, 1968. MR 37:6524
  • 2. H. Donnelly, Dirichlet problem at infinity for harmonic maps: Rank one symmetric spaces, Transactions of the American Mathematical Society 344 (1994), 713-735. MR 95c:58045
  • 3. M. Economakis, A counterexample to uniqueness and regularity for harmonic maps between hyperbolic spaces, Journal of geometric analysis 3 (1993), 27-36. MR 93m:58024
  • 4. P. Li and L. F. Tam, Uniqueness and regularity of proper harmonic maps, Ann. Math. 137 (1993), 167-201. MR 93m:58027
  • 5. G. Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies, 78, Princeton University Press, (1973). MR 52:5784
  • 6. M. Wolf, Infinite energy harmonic maps and degeneration of hyperbolic surfaces in moduli space, J. Diff. Geom. 33 (1991), 487-539. MR 92b:58055

Similar Articles

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

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


Additional Information

Harold Donnelly
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

DOI: https://doi.org/10.1090/S0002-9939-99-04627-4
Received by editor(s): April 19, 1997
Received by editor(s) in revised form: July 31, 1997
Additional Notes: The author was partially supported by NSF Grant DMS-9622709.
Communicated by: Peter Li
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society