Parabolic bundles and spherical metrics

de Borbon, Martin; Panov, Dmitri

doi:10.1090/proc/16052

Parabolic bundles and spherical metrics
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by Martin de Borbon and Dmitri Panov PDF

Proc. Amer. Math. Soc. 150 (2022), 5459-5472 Request permission

Abstract:

We use the Kobayashi-Hitchin correspondence for parabolic bundles to reprove the results of Troyanov [Trans. Amer. Math. Soc. 324 (1991), pp. 793-821] and Luo-Tian [Proc. Amer. Math. Soc. 116 (1992), pp. 1119-1129] regarding existence and uniqueness of conformal spherical metrics on the Riemann sphere with prescribed cone angles in the interval $(0, 2\pi )$ at a given configuration of three or more points.

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