منابع مشابه
Incompressibility and Least-area Surfaces
We show that if F is a smooth, closed, orientable surface embedded in a closed, orientable 3-manifold M such that for each Riemannian metric g on M , F is isotopic to a least-area surface F (g), then F is incompressible.
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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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Suppose mu and v are arcs whose union is an arc alpha and whose intersection is an arc beta. Suppose further that mu and v, respectively, lie in the boundaries of the disks M and N. It is shown that either alpha lies on the boundary of a disk or mu and v, respectively, lie in the boundaries of disks M' and N' which meet only in the arc beta. The construction is basic to recent results exploring...
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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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Subdivision surface intersections can be costly to compute. They require the intersection of high resolution meshes in order to obtain accurate results, which can lead to slow performance and high memory usage. In this paper we show how the strong convex hull property can lead to a method for efficiently computing intersections at high resolutions. Consequently, the method can be used with any ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1992
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1992.152.119