On Bloch’s constant

@article{Chen1996OnBC,
  title={On Bloch’s constant},
  author={Huai Hui Chen and Paul M. Gauthier},
  journal={Journal d’Analyse Math{\'e}matique},
  year={1996},
  volume={69},
  pages={275-291}
}
The well-known lower estimate for Bloch’s constantB is thatB > √3/4. Recently, M. Bonk has improved this estimate by showing thatB > √3/4 + 10-14. We give a further improvement by showing thatB ≥√3/4 + 2 × 10-14. 

Bloch's Constant is Computable

We prove the computability of Bloch's constant by presenting the first algorithm approximating the constant up to arbitrary precision.

Bloch constants for planar harmonic mappings

We give a lower estimate for the Bloch constant for planar harmonic mappings which are quasiregular and for those which are open. The latter includes the classical Bloch theorem for holomorphic

On the Computability of Blochs Constant

  • Robert Rettinger
  • Computer Science, Mathematics
    Electron. Notes Theor. Comput. Sci.
  • 2008

On the sum of squares of the coefficients of Bloch functions

AbstractIn this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved.

The Landau–Bloch type theorems for planar harmonic mappings with bounded dilation

Bloch constant of holomorphic mappings on the unit polydisk of ℂn

In this paper, we give a definition of Bloch mappings defined in the unit polydisk Dn, which generalizes the concept of Bloch functions defined in the unit disk D. It is known that Bloch theorem

Coefficients problems for Bloch functions

In this article we give a survey on different methods to estimate the values of functionals in the coefficients of Bloch functions.

Some new results on planar harmonic mappings

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.

References

SHOWING 1-6 OF 6 REFERENCES

On a Class of Conformal Metrics

  • M. Heins
  • Mathematics
    Nagoya Mathematical Journal
  • 1962
Last year when I was preparing for course lectures the work of Ahlfors [1] which establishes that the Bloch constant is at least as large as it appeared to me that the resources of the theory of

On Bloch’s constant

The lower bound for Bloch's constant is slightly improved. Let H(D) denote the class of holomorphic functions in D := {z E C: Izi 0 such that there exists a number z0 E C and a region Q C D which is

Über die Blochsche Konstante und zwei verwandte Weltkonstanten

DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen,

On Bloch Functions

An extension of Schwarz’s lemma

and has the constant curvature -4. 2. Consider now an analytic function o =f(z) from the circle I zx < 1 to a Riemann surface W. The analyticity is expressed by the fact that every local parameter w