Mostrando recursos 1 - 20 de 159

  1. Heegaard Genus of the Connected Sum of M-small Knots

    Kobayashi, Tsuyoshi; Rieck, Yoav

  2. Error Estimates for Discrete Harmonic 1-forms over Riemann Surfaces

    Luo, Wei
    We derive $L^2$ error estimates of computing harmonic or holomorphic 1-forms over a Riemann surface via finite element methods. Locally constant finite elements and first order approximations of the Riemann surface by triangulated meshes are considered. We use in the proof a Bochner type formula and a refined Poincaré inequality over a triangle of arbitrary shape.

  3. Dehn Filling of the "Magic" 3-manifold

    Martelli, Bruno; Petronio, Carlo
    We classify all the non-hyperbolic Dehn fillings of the complement of the chain link with three components, conjectured to be the smallest hyperbolic 3-manifold with three cusps. We deduce the classification of all non-hyperbolic Dehn fillings of infinitely many one-cusped and two-cusped hyperbolic manifolds, including most of those with smallest known volume. ¶ Among other consequences of this classification, we mention the following: ¶ · for every integer $n$, we can prove that there are infinitely many hyperbolic knots in S3 having exceptional surgeries ${n, n + 1, n + 2, n + 3}$, with $n + 1, n + 2$ giving small...

  4. Wave 0-trace and Length Spectrum on Convex Co-compact Hyperbolic Manifolds

    Guillarmou, Colin; Naud, Frédéric
    For convex co-compact hyperbolic quotients $\Gamma/\Bbb{H}^{n+1}$, we obtain aformula relating the 0-trace of the wave operator with the resonances and some conformal invariants of the boundary, generalizing a formula of Guillopé and Zworski in dimension 2. Then, by writing this 0-trace with the length spectrum, we prove precise asymptotics of the number of closed geodesics with an effective, exponentially small error term when the dimension of the limit set of $/Gamma$ is greater than $n/2$.

  5. Harmonic Mean Curvature Flow on Surfaces of Negative Gaussian Curvature

    Daskalopoulos, Panagio; Hamilton, Richard

  6. A Note on Perelman's Li-Yau-Hamilton Inequality

    Ni, Lei
    We give a proof to the Li–Yau–Hamilton-type inequality claimed by Perelman on the fundamental solution to the conjugate heat equation. The rest of the paper is devoted to improving the known differential inequalities of Li–Yau–Hamilton type via monotonicity formulae.

  7. Harmonic morphisms between Weyl spaces and twistorial maps

    Loubeau, Eric; Pantilie, Radu
    We show that Weyl spaces provide a natural context for harmonic morphisms, and we give the necessary and sufficient conditions under which on an Einstein–Weyl space of dimension 4 there can be defined, locally, at least five distinct foliations of dimension 2 which produce harmonic morphisms (Theorem 7.4). Also, we describe the harmonic morphisms between Einstein–Weyl spaces of dimensions 4 and 3 (Theorem 7.6).

  8. Erratum to "A remark on lower bound of Milnor number and characterization of homogeneous hypersurface singularities"

  9. Weil-Petersson volumes of the moduli spaces of CY manifolds

    Todorov, Andrey
    In this paper, it is proved that the volumes of the moduli spaces of polarized Calabi-Yau manifolds with respect to Weil-Petersson metrics are rational numbers. Mumford introduce the notion of a good metric on vector bundle over a quasi-projective variety in Hirzebruch’s proportionality principle in the non-compact case (D. Mumford, Inv. Math. 42 (1977), 239–272). He proved that the Chern forms of good metrics define classes of cohomology with integer coefficients on the compactified quasi-projective varieties by adding a divisor with normal crossings. Viehweg proved that the moduli space of CY manifolds is a quasi-projective variety. The proof that the...

  10. Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary

    Marques, Fernando C.

  11. Miyaoka-Yau-type inequalities for Kähler-Einstein manifolds

    Chan, Kwokwai; Leung, Naichung Conan
    We investigate Chern number inequalities on Kähler-Einstein manifolds and their relations to uniformization. For Kähler-Einstein manifolds with $c_1$ < 0, we prove certain Chern number inequalities in the toric case. For Kähler-Einstein manifolds with $c_1$ > 0, we propose a series of Chern number inequalities, interpolating Yau’s and Miyaoka’s inequalities.

  12. Global geometry of regions and boundaries via skeletal and medial integrals

    Damon, James

  13. Moduli space theory for constant mean curvature surfaces immersed in space-forms

    Gonçalves, Alexandre; Uhlenbeck, Karen
    In this short article we describe a local parametrization of the space of solutions of the Gauss-Coddazzi equations for constant mean curvature immersions of a Riemann surface into space-forms in codimension 1. The parameter space are cohomology classes of the holomorphic tangent bundle of the surface.

  14. A theorem of Hopf and the Cauchy-Riemann inequality

    Alencar, Hilario; do Carmo, Manfredo; Tribuzy, Renato
    Recently, Abresch and Rosenberg (A Hopf differential for constant mean curvature surfaces in $S/sp 2 x \Bbb R$ and $H/sp 2 x \Bbb R$ (U. Abresch, R. Rosenberg, Acta Math. 193 (2004), no. 2, 141–174) have extended Hopf’s Theorem on constant mean curvature to 3-dimensional spaces other than the space forms. Here we show that, rather than assuming constant mean curvature, it suffices to assume an inequality on the differential of the mean curvature.

  15. A generalization of Liu-Yau’s quasi-local mass

    Wang, Mu-Tao; Yau, Shing-Tung
    In Positivity of quasi-local mass (C.-C. M. Liu, S.-T. Yau, Phys. Rev. Lett. 90(23) (2003), 231102, 4) and Positivity of quasi-local mass II (C.-C. M. Liu, S.-T. Yau, J. Amer. Math. Soc. 19(1) (2006), 181–204), Liu and the second author propose a definition of the quasi-local mass and prove its positivity. This is demonstrated through an inequality which in turn can be interpreted as a total mean curvature comparison theorem for isometric embeddings of a surface of positive Gaussian curvature. The Riemannian version corresponds to an earlier theorem of Shi and Tam (Positive mass theorem and the boundary behavior of...

  16. Minimal Lagrangian surfaces in $\Bbb S\sp 2 x $\Bbb S\sp 2$

    Castro , Ildefonso; Urbano, Francisco
    We deal with the minimal Lagrangian surfaces of the Einstein-Kähler $\Bbb S\sp 2 x \Bbb S\sp 2$ surface, studying local geometric properties and showing that they can be locally described as Gauss maps of minimal surfaces in $\Bbb S\sp 2 \subset \Bbb R\sp 4$ . We also discuss the second variation of the area and characterize the most relevant examples by their stability behaviour.

  17. Type II ancient solutions to the Ricci flow on surfaces

    Chu, Sun-Chin
    Type II (ancient) solutions to the Ricci flow on surfaces are not yet classified. It is conjectured that the Rosenau solution and the cigar are the only solutions, modulo scaling. In this paper, we mainly study the backward limit and the circumference at spatial infinity of Type II ancient solutions on noncompact surfaces.

  18. A general gap theorem for submanifolds with parallel mean curvature in $R\sp {n+1}$

    Xu, Hong-wei; Gu, Juan-ru

  19. An invariant for triples in the Shilov boundary of a bounded symmetric domain

    Clerc, Jean-Louis

  20. Non-negatively curved Kähler manifolds with average quadratic curvature decay

    Chau, Albert; Tam, Luen-Fai
    Let $(M,g)$ be a complete noncompact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. Extending our techniques developed in A. Chau and L.-F. Tam. "On the complex structure of Kähler manifolds with non-negative curvature," we prove that the universal cover $\tilde M$ of $M$ is biholomorphic to $\Bbb{C}^2$ provided either that $(M,g)$ has average quadratic curvature decay, or $M$ supports an eternal solution to the Kähler–Ricci flow with non-negative and uniformly bounded holomorphic bisectional curvature. We also classify certain local limits arising from the Kähler–Ricci flow in the absence of uniform estimates on the injectivity radius.

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