Filling area conjecture and ovalless real hyperelliptic surfaces

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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.
21 pages, 3 figures, to appear in Geometric and Functional Analysis (GAFA)

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Differential Geometry, Geometric Topology, Metric Geometry, 53C23; 57N65; 52C07

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http://salesiana.dossiersoluciones.com/handle/123456789/71385

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0405583
 http://arxiv.org/abs/math/0405583

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arXiv