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Spherical surfaces with conical points: systole inequality and moduli spaces with many connected components

Research output: Contribution to journalArticle

Gabriele Mondello, Dmitri Panov

Original languageEnglish
Pages (from-to)1110-1193
Number of pages84
JournalGEOMETRIC AND FUNCTIONAL ANALYSIS
Volume29
Issue number4
Early online date8 Jul 2019
DOIs
Accepted/In press28 Apr 2019
E-pub ahead of print8 Jul 2019
Published1 Aug 2019

Bibliographical note

63 pages, 22 figures; minor revision of the previous version. Accepted for publication on GAFA

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Abstract

In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider some features of the forgetful map from the above moduli space of spherical surfaces with conical points to the associated moduli space of pointed Riemann surfaces, such as its properness, which follows from an explicit systole inequality that relates metric invariants (spherical systole) and conformal invariant (extremal systole).

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