Complete area minimizing minimal surfaces which are not totally geodesic
نویسندگان
چکیده
منابع مشابه
Compressing totally geodesic surfaces
In this paper we prove that one can find surgeries arbitrarily close to infinity in the Dehn surgery space of the figure eight knot complement for which some immersed totally geodesic surface compresses. MSC: 57M25, 57M50
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We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.
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It is conjectured that a hyperbolic knot complement does not contain a closed embedded totally geodesic surface. In this paper, we show that there are no such surfaces in the complements of hyperbolic 3-bridge knots and double torus knots. Some topological criteria for a closed essential surface failing to be totally geodesic are given. Roughly speaking, sufficiently ‘complicated’ surfaces can ...
متن کاملProving the absence of certain totally geodesic surfaces
We have proven the absence of totally geodesic surfaces bounded or punctured by either the figure-eight knot or the 62 link. We’ve also found a case (Borromean Rings checkerboard) in which a Dehn filling changes a surface that is not totally geodesic into one that is.
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1984
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1984.111.35