Maximal open radius for Strebel point

Abstract

Let $$T(S)$$ be the Teichmuller space of a hyperbolic Riemann surface $$S$$ . As is well known, when $$T(S)$$ is infinite-dimensional, the set $$\mathcal {SP}$$ of Strebel points is open and dense. Given a Strebel point $$[f]$$ in $$T(S)$$ , we prove that the the maximal radius of the open ball contained in $$\mathcal {SP}$$ and centered at $$[f]$$ is $$\frac{1}{4}\log \frac{K_0([f])}{H([f])}$$ . It is surprising that the boundary sphere of the maximal open ball is contained in $$\mathcal {SP}$$ . As a consequence, any open Strebel ball has no non-Strebel points as its boundary points. The infinitesimal version is also obtained.