1) La descarga del recurso depende de la página de origen
2) Para poder descargar el recurso, es necesario ser usuario registrado en Universia

Opción 1: Descargar recurso

Detalles del recurso


One of the most important results in Teichmüller theory is Royden’s theorem, which says that the Teichmüller and Kobayashi metrics agree on the Teichmüller space of a given closed Riemann surface. The problem that remained open is whether the Carathéodory metric agrees with the Teichmüller metric as well. In this article, we prove that these two metrics disagree on each $\mathcal{T}_{g}$ , the Teichmüller space of a closed surface of genus $g\ge2$ . The main step is to establish a criterion to decide when the Teichmüller and Carathéodory metrics agree on the Teichmüller disk corresponding to a rational Jenkins–Strebel differential $\varphi$ . First, we construct a holomorphic embedding $\mathcal{E}:\mathbb{H}^{k}\to\mathcal{T}_{g,n}$ corresponding to $\varphi$ . The criterion says that the two metrics agree on this disk if and only if a certain function $\mathbf{\Phi}:\mathcal{E}(\mathbb{H}^{k})\to\mathbb{H}$ can be extended to a holomorphic function $\mathbf{\Phi}:\mathcal{T}_{g,n}\to\mathbb{H}$ . We then show by explicit computation that this is not the case for quadratic differentials arising from $L$ -shaped pillowcases.

Pertenece a

Project Euclid (Hosted at Cornell University Library)  


Markovic, Vladimir - 

Id.: 70982996

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveCarathéodory metric - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 Duke University Press

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0012-7094
[References] 1547-7398

Fecha de contribución: 17-mar-2018


* Duke Math. J. 167, no. 3 (2018), 497-535
* doi:10.1215/00127094-2017-0041

Otros recursos del mismo autor(es)

  1. Carathéodory’s metrics on Teichmüller spaces and L-shaped pillowcases One of the most important results in Teichmüller theory is Royden’s theorem, which says that the Tei...
  2. Heat flows on hyperbolic spaces In this paper we develop new methods for studying the convergence problem for the heat flow on negat...
  3. Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk We prove that it is not possible to extend, in a homomorphic fashion, each quasisymmetric homeomorph...
  4. Classification of continuously transitive circle groups Let [math] be a closed transitive subgroup of [math] which contains a non-constant continuous path [...
  5. Counting essential surfaces in a closed hyperbolic three-manifold Let [math] be a closed hyperbolic three-manifold. We show that the number of genus  [math] surface s...

Otros recursos de la mismacolección

  1. Almost sure multifractal spectrum of Schramm–Loewner evolution Suppose that $\eta$ is a Schramm–Loewner evolution ( $\operatorname{SLE}_{\kappa}$ ) in a smoothly b...
  2. Galois and Cartan cohomology of real groups Suppose that $G$ is a complex, reductive algebraic group. A real form of $G$ is an antiholomorphic i...
  3. Group cubization We present a procedure of group cubization: it results in a group whose features resemble some of th...
  4. Odd degree number fields with odd class number For every odd integer $n\geq3$ , we prove that there exist infinitely many number fields of degree $...
  5. Regularization under diffusion and anticoncentration of the information content Under the Ornstein–Uhlenbeck semigroup $\{U_{t}\}$ , any nonnegative measurable $f:\mathbb{R}^{n}\to...

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.