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

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 sp...

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Published inGeometric and functional analysis Vol. 29; no. 4; pp. 1110 - 1193
Main Authors Mondello, Gabriele, Panov, Dmitri
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2019
Springer Nature B.V
Subjects
Analysis
Invariants
Mathematics
Mathematics and Statistics
Riemann surfaces
Singularity (mathematics)
Systole
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Summary: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).
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-019-00506-3