Recursos de colección
Kobayashi, Tsuyoshi; Rieck, Yoav
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.
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...
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 $n/2$.
Daskalopoulos, Panagio; Hamilton, Richard
Ni, Lei
We give a proof to the LiYauHamilton-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 LiYauHamilton type via monotonicity formulae.
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 EinsteinWeyl 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 EinsteinWeyl spaces of dimensions 4 and 3 (Theorem 7.6).
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 Hirzebruchs proportionality principle in the non-compact case (D. Mumford, Inv. Math. 42 (1977), 239272). 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...
Marques, Fernando C.
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 Yaus and Miyaokas inequalities.
Damon, James
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.
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, 141174) have extended Hopfs 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.
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), 181204), 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...
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.
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.
Xu, Hong-wei; Gu, Juan-ru
Clerc, Jean-Louis
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 KählerRicci flow with non-negative and uniformly bounded holomorphic bisectional curvature. We also classify certain local limits arising from the KählerRicci flow in the absence of uniform estimates on the injectivity radius.