What is it about?
In pure mathematics we often start with an example, and then write a definition, to encapsulate the features of that example. But then it is hard to know how many other examples are covered under the same umbrella. In this paper we show that if a projective surfaces fits a certain hyperbolicity condition, then it is actually a hyperbolic surface (up to blowing some bubbles on it).
Photo by Drew Beamer on Unsplash
Why is it important?
Projective structures are a geometric tool for the study of differential equations and group representations on Riemann surfaces. Certain classes of equations require the presence of singularities (i.e. branch points), and our results provide a better understanding of the geometric origins of this singular behavior, under some hyperbolicity conditions.
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This page is a summary of: Bubbling complex projective structures with quasi-Fuchsian holonomy, Journal of Topology and Analysis, September 2019, World Scientific Pub Co Pte Lt, DOI: 10.1142/s1793525320500326.
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