Abstract
We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Avilés, P., Choi, H.I., Micallef, M.: Boundary behavior of harmonic maps on non-smooth domains and complete negatively curved manifolds. J. Funct. Anal. 99, 293–331 (1991)
Giaquinta, M., Hildebrandt, S.: An existence theorem for harmonic mappings of Riemannian manifolds. J. Reine Angew. Math. 336, 124–164 (1982)
Hildebrandt, S., Kaul, H., Widman, K.: An existence theorem for harmonic mappings of Riemannian manifolds. Acta. Math. 138, 1–16 (1977)
Sario, L., Nakai, M.: Classification Theory of Riemann Surfaces. Springer Verlag, Berlin, Heidelberg, New York (1970)
Sung, C.J., Tam, L.F., Wang, J.: Bounded harmonic maps on a class of manifolds. Proc. Amer. Math. Soc. 124, 2241–2248 (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2012006926).
Rights and permissions
About this article
Cite this article
Lee, Y.H. Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary. Potential Anal 41, 463–468 (2014). https://doi.org/10.1007/s11118-013-9377-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11118-013-9377-2