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Calabi-Yau domains in three manifolds

By Francisco Martin and William H. Meeks III


We prove that given any compact Riemannian 3-manifold with boundary M, there exists a smooth properly embedded one-manifold G, included in M, each of whose components is a simple closed curve and such that the domain D=Int(M)-G does not admit any properly immersed open surfaces with at least one annular end, bounded mean curvature, compact boundary (possibly empty) and a complete induced Riemannian metric.Comment: 13 pages, 4 figure

Topics: Mathematics - Differential Geometry, 53A10 (Primary), 49Q05, 49Q10, 53C42 (Secondary)
Year: 2009
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