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 ...
متن کاملThe Existence of Least Area Surfaces in 3-manifolds
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...
متن کاملKnot Invariants in 3-manifolds and Essential Tori
Given a three-manifold M and a cohomology class τ ∈ H(M,Z/nZ), there is a naturally defined invariant of singular knots in M with exactly one double point, Vτ . It has been known that for some manifolds Vτ is integrable and that in these cases it defines an easily computed and highly effective knot invariant. This paper provides necessary and sufficient conditions on M for the integrability of ...
متن کاملFinite Covers of 3-manifolds Containing Essential Tori
It is shown in this paper that if a Haken 3-manifold contains an incompressible torus that is not boundary-parallel then either it has a finite cover that is a torus-bundle over the circle or it has finite covers with arbitrarily large first Betti number. In [He 4], Hempel conjectures that every Haken 3-manifold has a finite cover whose fundamental group has a nontrivial representation to the i...
متن کاملm at h . D G ] 2 1 A pr 1 99 8 LEAST AREA TORI AND 3 - MANIFOLDS OF NONNEGATIVE SCALAR CURVATURE : THE C ∞ CASE
The following conjecture arises from remarks in Fischer-Colbrie-Schoen ([FCS], Remark 4, p. 207): If (M, g) is a complete Riemannian 3-manifold with nonnegative scalar curvature and if Σ is a two-sided torus in M which is suitably of least area then M is flat. Such a result, as Fischer-Colbrie and Schoen commented, would be an interesting analogue of the Cheeger-Gromoll splitting theorem. Here ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1992-1131040-0