Asymptotic properties of energy of harmonic maps on asymptotically hyperbolic manifolds

Details Asymptotic properties of energy of harmonic maps on asymptotically hyperbolic manifolds Asymptotic properties of energy of harmonic maps on asymptotically hyperbolic manifolds

1996-10-30

arxiv.org/abs/dg-ga/9610020v1

Mathematics

Differential Geometry

LaTeX, 17 pages

Scientific paper

Asymptotic behavior of energy of a harmonic map defined on an asymptotically
hyperbolic manifold is considered. Using the growth of energy, we show that a
harmonic map defined on some asymptotically hyperbolic manifolds has to be
constant if the total energy is finite, or if the map approaches a point fast
enough, in terms of a defining function for the boundary.

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