A distortion theorem for bounded univalent functions.
A new characterization of Gromov hyperbolicity for negatively curved surfaces.
In this paper we show that to check Gromov hyperbolicity of any surface of constant negative curvature, or Riemann surface, we only need to verify the Rips condition on a very small class of triangles, namely, those obtained by marking three points in a simple closed geodesic. This result is, in fact, a new characterization of Gromov hyperbolicity for Riemann surfaces.
A note on a theorem of Chuaqui and Gevirtz.
A remark on polygonal quasiconformal maps.
Apollonian isometries of regular domains are Möbius mappings.
Best constants for metric space inversion inequalities
For every metric space (X, d) and origin o ∈ X, we show the inequality I o(x, y) ≤ 2d o(x, y), where I o(x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d o is a metric subordinate to I o, and x, y ∈ X o The constant 2 is best possible.
BMO-invariance of quasiminimizers.
Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
We survey variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a Legendre family of elliptic curves, the curvature form of the relative Bergman kernel metric is equal to the Poincaré metric on ℂ 0,1. The cases of other elliptic curves are either the same or trivial. Two proofs depending on elliptic functions’ special properties and Abelian differentials’ Taylor expansions are discussed, respectively. For a holomorphic family of hyperelliptic nodal or cuspidal curves...
Bundles and finite foliations.
Convex bodies of constant width and the Apollonian metric.
Discrete groups and thin sets.
Domains with convex hyperbolic radius.
Equivalence of the Apollonian and its inner metric.
Euclidean quasiconvexity.
Finite parts of the spectrum of a Riemann surface.
Generalized mean porosity and dimension.
Geodesics on Riemann surfaces with ramification points of order greater than two.
Gromov hyperbolicity of certain conformal invariant metrics.
Harmonic diffeomorphisms and Teichmüller theory.
Inégalités isosystoliques conformes.