Surfaces of Prescribed Mean Curvature in Quasi-Fuchsian Manifolds

Details Surfaces of Prescribed Mean Curvature in Quasi-Fuchsian Manifolds Surfaces of Prescribed Mean Curvature in Quasi-Fuchsian Manifolds

2010-03-08

arxiv.org/abs/1003.1546v1

Mathematics

Differential Geometry

16 pages

Scientific paper

Let $M$ be a quasi-Fuchsian three-manifold that contains a closed incompressible surface with principal curvatures within the range of the unit interval, for a prescribed function $H$ (with mild conditions) on $M$, we construct a closed incompressible surface with mean curvature $H$ . A direct application is the existence of embedded surfaces of prescribed constant mean curvatures with constants in $(-2,2)$.

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