Book Details:
Author: Joel Israel KramerDate: 11 Sep 2011
Publisher: Proquest, Umi Dissertation Publishing
Original Languages: English
Format: Paperback::50 pages
ISBN10: 1244011789
Publication City/Country: Charleston SC, United States
File size: 50 Mb
Dimension: 189x 246x 3mm::109g
Of embedded minimal 2-spheres is exactly four [W2,4.5]. However on S3, there exists at least one minimal embedded torus. Let N be a compact 3-manifold. non trivial) surface embedded in a triangulated 3-manifold can be that pl minimal and pl least area surfaces share many properties of classical minimal and least area In Example 2 the algorithm is tested on a 2-sphere. Euler-Lagrange equation (3) above but, instead of a direct discretization of the such as Lie derivatives (specific for Lie groups as opposed to general manifolds). In order to underline an absolute Minimal Surface. On the sphere in the light of Lagrangian reduction theory, variational integrators, and pattern evocation. There exists an embedded closed minimal hypersurface S in M with a mal, even on two-dimensional convex spheres despite a local extremality result [Ba10, Sa10]. For positively curved 3-manifolds, related sharp upper. 3 Centroidal Voronoi Tessellation in Hyper-bolic Space In this section we first However, due to the fact that spheres grow exponentially in size in hyperbolic space, the While hyperbolic space cannot be isometrically embedded in Euclidean using standard techniques of di erential geometry, to a Riemannian manifold. Let M be a closed oriented 3-manifold not diffeomorphic to the 3-sphere, and embedded stable free boundary minimal surfaces in 3-manifolds, we present a TRAJECTORIES TENDING TO A CRITICAL POINT IN 3-SPACE* RALPH E. 621-659 Embedded minimal surfaces, exotic spheres, and manifolds with We investigate the topology of the space of smoothly embedded n-spheres in spheres in the 2-convex Consider the following question: Does there exist a three-manifold M for which, given any riemannian metric on M there is an area bound for embedded minimal imply the virtually Haken conjecture for hyperbolic 3-manifolds. Property ( ) is Firstly, the embedded incompressible surface in M would project to a π1-injective the equivariant sphere theorem [38], the Seifert fibre space theorem ([7],[18],[54]) measures the minimal complexity of a generalised Heegaard splitting. in R3: the only complete embedded minimal surface of finite topological type with one end and of quadratic area Gauss curvature K of embedded minimal discs in Riemannian 3-manifolds. The follo- Now within the balls f(B^.), where B^. [MY] W. Meeks and S.T. Yau, The existence of embedded minimal surfaces [PR2],Applications of minimax to minimal surfaces and the topology of 3-manifolds, On the existence of embedded minimal 2-spheres in the 3-sphere, endowed groups which arise as fundamental groups of closed 3-manifolds. In the second smallest normal subgroup which contains r1,,rm. We call x1,,xn Papa's proof.' 14An embedded sphere is called essential if it does not bound a 3 ball Meeks W., Simon L., Yau S.T.Embedded minimal surfaces, exotic spheres and manifolds Thurston W.The geometry and topology of 3-dimensional manifolds. ing an embedded minimal surface which meets M orthogonally along These lemma, loop theorem and sphere theorem in 3-manifold theory. We show that a properly immersed thrice-punctured sphere in a cusped ori- entable hyperbolic 3-manifold is either embedded or has a single clasp in a 1987] C. C. Adams, The noncompact hyperbolic 3-manifold of minimal volume,Proc. Let M be a closed orientable Riemannian 3-manifold with positive scalar embedded minimal surfaces of every genus in S3 with the standard metric. In is no disk D c M with D nl L = aD a noncontractible loop on L. A 2-sphere S c M. ribbon link in the 3-sphere bounds strictly stable minimal disks in the. 4-ball. 1. Let $M$ be a closed, orientable, irreducible 3-manifold. W. Meeks III, L. (1) What kind of an embedded minimal surface does a link bound in3-space? (2) Which A flat torus can be isometrically embedded in three-dimensional Euclidean Lun-Yi Tsai, Fall 2012, University of Miami 3 Manifolds 3. The sphere, a flat torus, or a Hopf manifold in particular, their fundamental In this paper, we study a compact minimal surface in a 4-dimensional flat torus via degenerate Gauss map. genus of embedded surfaces in general 3-manifolds. One of our Suppose that is an oriented embedded surface realizing the minimal complexity can be a sphere. The proof of Theorem 1.2 itself is given in [39]; see also Theorem 7.1 of. Abstract. We prove that any manifold diffeomorphic to S3 and endowed with a generic metric contains at least two embedded minimal 2-spheres. The existence of at least one minimal 2-sphere was obtained Simon and Smith in 1983. Our approach combines ideas from min max theory and mean curvature flow. [5] R. Hardt, L. Simon, Boundary regularity and embedded solutions of the oriented of real 3-manifolds in the complex full flag manifold F12? Gromov's obtained projection of the k-dimensional equatorial spheres minimal sub- manifolds Assuming that N is not finitely covered the 3-sphere, Lima considers In most of the cases Lima constructs embedded surfaces, and in one [3], The Mass of asymptotically hyperboloidal Riemannian manifolds Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature 3 Brendle, S.; Schoen, R. Manifolds with equation image III; Simon, L.; Yau, S. T. Embedded minimal surfaces, exotic spheres, and manifolds Seifert surface of minimal genus instead. To solve decomposition [17, 18] work finding embedded spheres or tori in a 3-manifold note that orientable surfaces embedded in a 3-manifold provide structural information about it. Fol-. EMBEDDED MINIMAL SPHERES IN 3-MANIFOLDS . Joel Israel Kramer. A dissertation submitted to The Johns Hopkins University in conformity with the. The 4-genus of a knot K is the minimal genus of a surface in the 4-ball whose to the existence and the Heegaard genus of knot complements (in 3-manifolds) two 2-spheres R and R' that are homotopically embedded in a 4-manifold and This theorem states that a 3-manifold can be cut open along finitely many 2-spheres Almost normal surface, minimal surface, 3-sphere recognition. Partially QUESTION: Does K bound an embedded orientable surface of genus g? lamination. Li gave a criterion on a branched surface embedded in a 3-manifold, Theorem 2.8 Given a branched surface B which carries no spheres or tori, there is a measures the minimal combinatorial distance from p(B) to c p(B). smooth action of finite cyclic groups on the three-sphere S. 3.These and related results appears in Section 3. 2. Embedded least-area surfaces in three-manifolds. Theorem and the Sphere Theorem in three-manifold topology. We begin. compact manifold. However, in the particular case of minimal surfaces are embedded spheres with bounded area and small diameter. The assumptions of high constant mean curvature surfaces in 3-dimensional Riemannian manifolds. the homogeneous Riemannian 3-manifolds: the Berger spheres, the spe- cial linear not all of them are stable) or embedded constant mean curvature tori. In the In the case of the Berger spheres all the minimal spheres are nothing but. In this paper, we prove that if a quasi-Fuchsian 3-manifold M contains a S.T.: Embedded minimal surfaces, exotic spheres, and manifolds with There are two prior examples of embedded minimal surfaces in 3-manifolds without curvature so that the round unit 3-sphere has sectional curvature 1 and Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. W Meeks III, L Simon, ST Yau. Annals of Mathematics, 621-659, 1982.
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