arXiv subjects

T. Sugawa

Publications and source records attributed to T. Sugawa.

3 recordsLinked to original sources

arXiv2012

Radius problems associated with pre-Schwarzian and Schwarzian derivatives

Some of important univalence criteria for a non-constant meromorphic function $f(z)$ on the unit disk $\ID$ involve its pre-Schwarzian or Schwarzian derivative. We consider an appropriate norm for the pre-Schwarzian derivative, and discuss the problem of finding the largest possible $r\in (0,1)$ for which the pre-Schwarzian norm of the dilation $r^{-1}f(rz)$ is not greater than a prescribed number for normalized univalent functions $f(z)$ in the unit disk. Similar results concerning the Schwarzian derivative are also obtained

math.CV↗

arXiv2009

Twice-punctured hyperbolic sphere with a conical singularity and generalized elliptic integral

We describe, in terms of generalized elliptic integrals, the hyperbolic metric of the twice-punctured sphere with one conical singularity of prescribed order. We also give several monotonicity properties of the metric and a couple of applications.

math.CV↗

arXiv2008

Hypergeometric functions and hyperbolic metric

We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.

math.CV↗