Filling area conjecture and ovalless real hyperelliptic surfaces
Differential Geometry
2007-05-23 v2 Geometric Topology
Metric Geometry
Abstract
We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus 0. We translate the problem into a question about closed ovalless real surfaces. The conjecture then results from a combination of two ingredients. On the one hand, we exploit integral geometric comparison with orbifold metrics of constant positive curvature on real surfaces of even positive genus. Here the singular points are Weierstrass points. On the other hand, we exploit an analysis of the combinatorics on unions of closed curves, arising as geodesics of such orbifold metrics.
Cite
@article{arxiv.math/0405583,
title = {Filling area conjecture and ovalless real hyperelliptic surfaces},
author = {Victor Bangert and Christopher Croke and Sergei V. Ivanov and Mikhail G. Katz},
journal= {arXiv preprint arXiv:math/0405583},
year = {2007}
}
Comments
21 pages, 3 figures, to appear in Geometric and Functional Analysis (GAFA)