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On the existence of Hermitian-harmonic maps from complete Hermitian to complete Riemannian manifolds

by Grunau, Hans-Christoph, Kuehnel, Marco.

Series: 2003-09, Preprints

53C42 Immersions (minimal, prescribed curvature, tight, etc.)
35J60 Nonlinear elliptic equations
35K55 Nonlinear parabolic equations

On non-Kähler manifolds the notion of harmonic maps is modified
to that of Hermitian harmonic maps in order to be compatible with the complex
structure. The resulting semilinear elliptic system is not
in divergence form.

The case of noncompact complete preimage and target manifolds is
considered. We give conditions for existence and uniqueness of
Hermitian-harmonic maps and solutions of the corresponding
parabolic system, which observe the non-divergence form of
the underlying equations. Numerous examples illustrate the
theoretical results and the fundamental difference to
harmonic maps.

Hermitian-harmonic maps, non-Kaehler manifolds, non-divergence form

This paper was published in:
Math. Z. 249 , 297-327 (2005).