Least area incompressible surfaces in 3-manifolds
نویسندگان
چکیده
منابع مشابه
Least Area Incompressible Surfaces in 3-Manifolds
Let M be a Riemannian manifold and let F be a closed surface. A map f: F---,M is called least area if the area of f is less than the area of any homotopic map from F to M. Note that least area maps are always minimal surfaces, but that in general minimal surfaces are not least area as they represent only local stationary points for the area function. The existence of least area immersions in a ...
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This paper presents a new and unified approach to the existence theorems for least area surfaces in 3-manifolds. Introduction. A surface F smoothly embedded or immersed in a Riemannian manifold M is minimal if it has mean curvature zero at all points. It is a least area surface in a class of surfaces if it has finite area which realizes the infimum of all possible areas for surfaces in this cla...
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An incompressible bounded surface F on the boundary of a compact, connected, orientable 3-manifold M is arc-extendible if there is a properly embedded arc γ on ∂M − IntF such that F ∪ N(γ) is incompressible, where N(γ) is a regular neighborhood of γ in ∂M . Suppose for simplicity that M is irreducible and F has no disk components. If M is a product F × I, or if ∂M −F is a set of annuli, then cl...
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 1983
ISSN: 0020-9910,1432-1297
DOI: 10.1007/bf02095997