• Corpus ID: 233864814

A Schwarz-Type Lemma for Squeezing Function on Planar Domains

@inproceedings{Okten2021ASL,
  title={A Schwarz-Type Lemma for Squeezing Function on Planar Domains},
  author={Ahmed Yekta Okten},
  year={2021}
}
With an easy application of maximum principle, we establish a Schwarz-type lemma for squeezing function on finitely connected planar domains that directly yields the explicit formula for squeezing function on doubly connected domains obtained in [14] by Ng, Tang and Tsai. 

References

SHOWING 1-10 OF 18 REFERENCES
A note on the squeezing function
  • A. Solynin
  • Mathematics, Physics
    Proceedings of the American Mathematical Society
  • 2021
The squeezing problem on $\mathbb{C}$ can be stated as follows. Suppose that $\Omega$ is a multiply connected domain in the unit disk $\mathbb{D}$ containing the origin $z=0$. How far can the
The squeezing function on doubly-connected domains via the Loewner differential equation
For any bounded domains $$\varOmega $$ in $${\mathbb {C}}^{n}$$ , Deng, Guan and Zhang introduced the squeezing function $$S_\varOmega (z)$$ which is a biholomorphic invariant of bounded
Fridman Function, Injectivity Radius Function, and Squeezing Function
Very recently, the Fridman function of a complex manifold X has been identified as a dual of the squeezing function of X. In this paper, we prove that the Fridman function for certain hyperbolic
On the squeezing function for finitely connected planar domains
In a recent paper, Ng, Tang and Tsai (Math. Ann. 2020) have found an explicit formula for the squeezing function of an annulus via the Loewner differential equation. Their result has led them to
On the comparison of the Fridman invariant and the squeezing function.
Let $D$ be a bounded domain in $\mathbb{C}^n$, $n\ge 1$. In this paper, we study two biholomorphic invariants on $D$, the Fridman invariant $e_D(z)$ and the squeezing function $s_D(z)$. More
Fridman’s Invariant, Squeezing Functions, and Exhausting Domains
We show that if a bounded domain $\Omega$ is exhausted by a bounded strictly pseudoconvex domain $D$ with $C^2$ boundary, then $\Omega$ is holomorphically equivalent to $D$ or the unit ball, and show
A gap theorem for the complex geometry of convex domains
  • Andrew M. Zimmer
  • Mathematics
    Transactions of the American Mathematical Society
  • 2018
<p>In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex
A Domain with Non-plurisubharmonic Squeezing Function
We construct a strictly pseudoconvex domain with smooth boundary whose squeezing function is not plurisubharmonic.
Estimate of the squeezing function for a class of bounded domains
We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.
An Estimate for the Squeezing Function and Estimates of Invariant Metrics
We give estimates for the squeezing function on strictly pseudoconvex domains, and derive some sharp estimates for the Caratheodory, Sibony and Azukawa metrics near their boundaries.
...
1
2
...