On the classification of singular flat structures on surfaces
Ousama Malouf (IRMA)
TL;DR
This paper investigates the classification of flat surfaces with conical singularities, focusing on pairs of pants with one singular point, and discusses the decomposability of such surfaces.
Contribution
It provides a classification for flat structures on pairs of pants with a single singularity and explores the conditions for decomposing flat surfaces into pairs of pants.
Findings
Parameterization for flat structures on pairs of pants with one singularity
Discussion on decomposability of flat surfaces into pairs of pants
Insights into open questions about general flat surface parameters
Abstract
We study in this work flat surfaces with conical singularities, that is, surfaces provided with a flat structure with conical singular points. Finding good parameters for these surfaces in the general case is an open question. We give an answer to this question in the case of flat structures on pairs of pants with one singular point. The question of decomposability of an arbitrary flat surface into flat pairs of pants is discussed.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Point processes and geometric inequalities