Working on my current research problem, Teichmuller spaces for surfaces with cone points have come into play. It's fairly easy to formulate some of the definitions, a few basic results, etc. To be precise, I am looking to understand the Teichmuller space of a closed surface $M$ with genus $g$ and $b$ cone points with fixed cone angles $\theta\_1,\dots, \theta\_b \in (0,2\pi)$ such that $$\chi(M) - \sum\_j (2\pi - \theta\_j) < 0$$ (this last condition ensures there is a metric of constant curvature $-1$ away from the cone points). It would be nice to include punctures and boundary components, but I'll take what I can get.


I'm wondering if people have fleshed out the details for these spaces, and if so what are the best/standard sources? Some things should quite naturally carry over (for instance, Fenchel Nielsen coordinates), but I'm sure there must be some non-obvious subtleties. I'm simply asking as it would be quite the tedious task to do all this myself (but I suppose I will if the answer to my question is negative).



Teichmuller space for surface with cone points
Here are some recent papers:


Rafe Mazzeo, Hartmut Weiss
arXiv:1509.07608 
Teichmüller theory for conic surfaces


arXiv:1710.09781 Rafe Mazzeo and Xuwen Zhu,
Conical metrics on Riemann surfaces, I: the compactified configuration space and regularity.


