Classifications of some special infinity-harmonic maps.
Wang, Ze-Ping, Ou, Ye-Lin (2009)
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Wang, Ze-Ping, Ou, Ye-Lin (2009)
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Originally, harmonic morphisms were defined as continuous mappings φ:X → X' between harmonic spaces such that h'∘φ remains harmonic whenever h' is harmonic, see [1], p. 20. In general linear axiomatic potential theory, one has to replace harmonic functions h' by hyperharmonic functions u' in this definition, in order to obtain an interesting class of mappings, see [3], Remark 2.3. The modified definition appears to be equivalent with the original one, provided X' is a Bauer space, i.e.,...
Thomas Kappeler (2002)
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We consider perturbations of the harmonic map equation in the case where the source and target manifolds are closed riemannian manifolds and the latter is in addition of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. For generic perturbations the set of solutions is finite and we present a count of this set. An important ingredient for our...
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