Equivariant Plateau Problems

Graham Smith

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Submission date: 13. Feb. 2006
Pages: 85
published in: Geometric and functional analysis, 140 (2009) 1, p. 95-135 
DOI number (of the published article): 10.1007/s10711-008-9310-9
Bibtex
MSC-Numbers: 57M50, 30F10, 30F40, 32G15
Keywords and phrases: Kleinian groups, Fuchsian groups, plateau problem, complex projective structures, immersions
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Abstract:
Let (M,Q) be a compact, three dimensional manifold of strictly negative sectional curvature. Let be a compact, orientable surface of hyperbolic type (i.e. of genus at least two). Let be a homomorphism. Generalising a recent result of Gallo, Kapovich and Marden concerning necessary and sufficient conditions for the existence of complex projective structures with specified holonomy to manifolds of non-constant negative curvature, we obtain necessary conditions on for the existence of a so called -equivariant Plateau problem over , which is equivalent to the existence of a strictly convex immersion which realises (i.e. such that ).