TY - JOUR
T1 - Spherical surfaces with conical points
T2 - systole inequality and moduli spaces with many connected components
AU - Mondello, Gabriele
AU - Panov, Dmitri
N1 - 63 pages, 22 figures; minor revision of the previous version. Accepted for publication on GAFA
PY - 2019/8/1
Y1 - 2019/8/1
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=85068864643&partnerID=8YFLogxK
U2 - 10.1007/s00039-019-00506-3
DO - 10.1007/s00039-019-00506-3
M3 - Article
SN - 1016-443X
VL - 29
SP - 1110
EP - 1193
JO - GEOMETRIC AND FUNCTIONAL ANALYSIS
JF - GEOMETRIC AND FUNCTIONAL ANALYSIS
IS - 4
ER -