13 citations · 35 across the 28 of their papers we have counts for
31 papers
Quasiconformal deformations preserving Hilbert's norm and their applications
Samuel L Krushkal
This paper focuses on estimating the Taylor coefficients for Hilbert spaces of holomorphic functions on the disk using intrinsic features of univalent functions and of Teichmuller…
On Zalcman's and Bieberbach conjectures
Samuel L. Krushkal
The well-known Zalcman conjecture, which implies the Bieberbach conjecture, states that the coefficients of univalent functions on the u…
Towards a general distortion theory for univalent functions: Teichmuller spaces and coefficient problems of complex analysis
Samuel L. Krushkal
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and phy…
A link between covering and coefficient theorems for holomorphic functions
Samuel L. Krushkal
Recently the author presented a new approach to solving the coefficient problems for various classes of holomorphic functions , not necessarily…
The Grunsky operator and quasiconformality: old and new
Samuel L. Krushkal
The Grunsky operator arises from univalence and plays a crucial role in geometric function theory. This operator also implies quasiconformal extendibility and has an intrinsic conn…
Teichmuller balls and biunivalent holomorphic functions
Samuel L. Krushkal
Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations. T…
All Teichmuller spaces are not starlike
Samuel L. Krushkal
This paper is the final step in solving the problem of starlikeness of Teichmuller spaces in Bers' embedding. This step concerns the case of finite dimensional Teichmuller spaces $…
Polygons and non-starlikeness of Teichmuller spaces
Samuel L. Krushkal
The problem of starlikeness of Teichmuller spaces in Bers' embedding was raised in 1974 and is solved (negatively) for Teichmuller spaces of sufficiently large dimensions. The orig…
Quantitative theory of reflections across quasiconformal polygonal lines
Samuel L. Krushkal
The paper continues the author's research in the problem of quantitative investigation of basic curvelinear quasiinvariants of quasiconformal curves. It concerns polygons with infi…
The Grunsky norm of univalent functions and abelian holomorphic differentials
Samuel L. Krushkal
We establish that the Grunsky norm of any normalized univalent function on the disk is completely determined by the squares of holomorphic abelian differentials (in contrast to the…
Extremal properties of Sobolev's Beltrami coefficients and distortion of curvelinear functionals
Samuel L. Krushkal
An important problem in applications of quasiconformal analysis and in its numerical aspect is to establish algorithms for explicit or approximate determination of the basic quasii…
Quasiconformal deformations of nonvanishing functions and the Hummel-Scheinberg-Zalcman conjecture
Samuel L. Krushkal
Recently the author proved that the 1977 Hummel-Scheinberg-Zalcman conjecture on coefficients of nonvanishing functions is true for all , i.e., for…
Grunsky operator, Grinshpan's conjecture and universal Teichmuller space
Samuel L. Krushkal
A. Grinshpan posed a deep conjecture on the norm of the Grunsky operator generated by univalent functions in the disk. It gives a quantitative answer in terms of the Grunsky coeffi…
Teichmuller space theory and classical problems of geometric function theory
Samuel L. Krushkal
Recently the author presented a new approach to solving the coefficient problems for holomorphic functions based on the deep features of Teichmuller spaces. It involves the Bers is…
On holomorphic contractibility of Teichmuller spaces
Samuel L. Krushkal
The problem of holomorphic contractibilty of the Teichmuller spaces of punctured spheres () arose in the 1970s in connection with solving algebraic equations in Ba…
A new look at Krzyz's conjecture
Samuel L. Krushkal
Recently the author has presented a new approach to solving extremal problems of geometric function theory. It involves the Bers isomorphism theorem for Teichmuller spaces of punct…
Extremal quasiconformality vs rational approximation
Samuel L. Krushkal
We show that on most of the hyperbolic simply connected domains the weighted bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorp…
A general coefficient theorem for univalent functions
Samuel L. Krushkal
Using the Bers isomorphism theorem for Teichmuller spaces of punctured Riemann surfaces and some of their other complex geometric features, we prove a general theorem on maximizati…
A question of Kuhnau
Samuel L. Krushkal
It is well known that the square is not a Strebel's point (i.e., its extremal Beltrami coefficient is not Teichmuller). Many years ago, Reiner Kuhnau posed the question: does there…
Quasiconformal features and Fredholm eigenvalues of convex polygons
Samuel L. Krushkal
An important open problem in geometric complex analysis is to find algorithms for explicit determination of basic functionals intrinsically connected with conformal and quasiconfor…
Holomorphic contractibility of Teichmüller spaces
Samuel L. Krushkal
The problem of holomorphic contractibilty of Teichmüller spaces T(0, n) of the punctures spheres (n > 4) arose in the 1970s in connection with solving the algebraic equations in Ba…
Complex rigidity of Teichmüller spaces
Samuel L. Krushkal
We outline old and new results concerning the well-known problems in the Teichmüller space theory, i.e., whether these spaces are starlike in the Bers holomorphic embedding and whe…
Complex geodesics and variational calculus for univalent functions
Samuel L. Krushkal
It turns out that complex geodesics in Teichmüller spaces with respect to their invariant metrics are intrinsically connected with variational calculus for univalent functions. We…
Hyperbolic geodesics, Krzyz's conjecture and beyond
Samuel L. Krushkal
In 1968, Krzyz conjectured that for non-vanishing holomorphic functions in the unit disk with , we have the sharp bound …