Harmonic maps and singularities of period mappings

Harmonic maps and singularities of period mappings

We use simple methods from harmonic maps to investigate singularities of period mappings at infinity. More precisely, we derive a harmonic map version of Schmid’s nilpotent orbit theorem. MSC Classification 14M27, 58E20

Singularities of Harmonic Maps

This article surveys research on the existence, structure, behavior, and asymptotics of singularities of harmonic maps.

Nonunique Tangent Maps at Isolated Singularities of Harmonic Maps

Shoen and Uhlenbeck showed that “tangent maps” can be defined at singular points of energy minimizing maps. Unfortunately these are not unique, even for generic boundary conditions. Examples are discussed which have isolated singularities with a continuum of distinct tangent maps. Let Ω be a bounded domain in R (or more generally a compact riemannian manifold with boundary) and let N be a compa...

Harmonic maps on spaces with conical singularities

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Stability and singularities of harmonic maps into spheres