skip to main content

Attention:

The NSF Public Access Repository (PAR) system and access will be unavailable from 11:00 PM ET on Thursday, February 13 until 2:00 AM ET on Friday, February 14 due to maintenance. We apologize for the inconvenience.


Title: Uniform bounds for Weil-Petersson curvatures: UNIFORM BOUNDS FOR WEIL-PETERSSON CURVATURES
PAR ID:
10061730
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Oxford University Press (OUP)
Date Published:
Journal Name:
Proceedings of the London Mathematical Society
Volume:
117
Issue:
5
ISSN:
0024-6115
Page Range / eLocation ID:
p. 1041-1076
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. De Gruyter (Ed.)
    In this article we show that for every finite area hyperbolic surface X of type (g; n) and any harmonic Beltrami differential 􏰚 on X , then the magnitude of 􏰚 at any point of small injectivity radius is uniform bounded from above by the ratio of the Weil–Petersson norm of 􏰚 over the square root of the systole of X up to a uniform positive constant multiplication. We apply the uniform bound above to show that the Weil–Petersson Ricci curvature, restricted at any hyperbolic surface of short systole in the moduli space, is uniformly bounded from below by the negative reciprocal of the systole up to a uniform positive constant multiplication. As an application, we show that the average total Weil–Petersson scalar curvature over the moduli space is uniformly comparable to -g as the genus g goes to infinity. 
    more » « less
  2. null (Ed.)
  3. null (Ed.)
    Abstract In this paper we prove that the limit set of any Weil–Petersson geodesic ray with uniquely ergodic ending lamination is a single point in the Thurston compactification of Teichmüller space. On the other hand, we construct examples of Weil–Petersson geodesics with minimal non-uniquely ergodic ending laminations and limit set a circle in the Thurston compactification. 
    more » « less
  4. This is a companion to the paper "Weil-Petersson curves, conformal energies, beta-numbers, and minimal surfaces". That paper gives various new geometric characterizations of Weil-Petersson in the plane that can be extended to curves in all finite dimensional Euclidean spaces. This paper deals with the 2-dimensional case, giving new proofs of some known characterizations, and giving new results for the conformal weldings of Weil-Petersson curves and a geometric characterization of these curves in terms of Peter Jones's beta-numbers. 
    more » « less