On the Moduli Space of Singular Euclidean Surfaces
Marc Troyanov
TL;DR
This paper explores the deformation theory of singular Euclidean surfaces and uses it to construct new geometric structures on the moduli space of Riemann surfaces.
Contribution
It develops the deformation theory for piecewise flat structures and introduces novel geometric structures on moduli spaces.
Findings
Established a deformation framework for singular Euclidean surfaces
Constructed new geometric structures on moduli spaces
Enhanced understanding of surface deformation theory
Abstract
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometric and Algebraic Topology