Harmonic maps with noncontact boundary values

Donnelly, Harold

doi:10.1090/S0002-9939-99-04627-4

Harmonic maps with noncontact boundary values
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by Harold Donnelly

Proc. Amer. Math. Soc. 127 (1999), 1231-1241

DOI: https://doi.org/10.1090/S0002-9939-99-04627-4

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Abstract:

Every rank one symmetric space $M$, of noncompact type, admits a compactification $\overline M$ by attaching a sphere $S^{n-1}$ at infinity. If $M$ does not have constant sectional curvature, then $\overline M-M$ admits a natural contact structure. This paper presents a number of harmonic maps $h$, from $M$ to $M$, which extend continuously to $\overline M$, and have noncontact boundary values. If the boundary values are assumed continuously differentiable, then the contact structure must be preserved.

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