Abstract
The relationship between harmonic maps from R2 to S2, H2, ST,1, S1,1(−1) and the ± sinh — Laplace, ± sine — Laplace equation is found respectively. Existence theorems of some boundary value problems for the above harmonic maps are obtained. In the cases of H2, S1,1(+1), S1,1(−1) the results are global.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliography
Pohlmeyer, K.: Integrable Hamiltonian System and Interaction Through Quadratic Constraints. Comun.Math. Phys.46, 207–221 (1976)
Gu, C.H.: On the Cauchy Problem for Harmonic Map Defined on Two — Dimensional Minkowski Space. Comun. on Pure and Appl.Math.33, 727–737 (1980)
Gu, C.H.: On the Harmonic Maps from R1,1 to S1,1. to appear
Chern, S.S.: Geometrical Interpretation of Sinh — Gordon Equations. Annales Polinici Math.39, 63–69 (1981)
Courant, R. and Hilbert, D.: Methods of Mathematical Physics, vol II, 369–374 Interscience Publishers, (1966)
Author information
Authors and Affiliations
Additional information
Research supported partially by the Institute for Applied Mathematics, Sonderforschungsbereich 72 of the University of Bonn
Rights and permissions
About this article
Cite this article
Hesheng, H. Sine-Laplace equation, sink - Laplace equation and harmonic maps. Manuscripta Math 40, 205–216 (1982). https://doi.org/10.1007/BF01174876
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01174876