Journal article
On convergence to a football
Mathematische annalen, Vol.366(1-2), pp.83-100
10/13/2015
DOI: 10.1007/s00208-015-1303-z
Abstract
We show that spheres of positive constant curvature with
n
(
n
≥
3
) conic points converge to a sphere of positive constant curvature with two conic points [or called an (American) football] in Gromov–Hausdorff topology when the corresponding singular divisors converge to a critical divisor in the sense of Troyanov. We prove this convergence in two different ways. Geometrically, the convergence follows from Luo–Tian’s explicit description of conic spheres as boundaries of convex polytopes in
S
3
. Analytically, regarding the conformal factors as the singular solutions to the corresponding PDE, we derive the required a priori estimates and convergence result after proper reparametrization.
Details
- Title: Subtitle
- On convergence to a football
- Creators
- Hao Fang - University of IowaMijia Lai - Shanghai Jiao Tong University
- Resource Type
- Journal article
- Publication Details
- Mathematische annalen, Vol.366(1-2), pp.83-100
- DOI
- 10.1007/s00208-015-1303-z
- ISSN
- 0025-5831
- eISSN
- 1432-1807
- Publisher
- Springer Berlin Heidelberg
- Grant note
- DMS-100829 / National Science Foundation (US) (http://dx.doi.org/10.13039/100000001)
- Language
- English
- Date published
- 10/13/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9984241155702771
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