Gromov-Hausdorff limits of flat Riemannian surfaces

Autor:	Sustretov, Dmitry
Rok vydání:	2018
Předmět:	Mathematics - Algebraic Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	I study Gromov-Hausdorff limits of complex curves endowed with singular flat metrics of constant diameter. I formulate a criterion that the limit is collapsed in terms of a certain piecewise affine weight function on the dual intersection complex of a semi-stable model of the degeneration introduced by Kontsevich and Soibelman. I describe the collapsed and non-collapsed limits, which are, respectively, metric graphs and finite collections of complex curves with flat metrics glued along finitely many points. I show that the collapsed limit of any positive genus can occur. Comment: 17 pages. some fixes
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1802.03818 Zobrazit plný text záznamu View this record from Arxiv