The radius of convexity of certain analytic functions. II.
The radius of starlikeness for convex functions of complex order.
The radius of starlikeness of the certain classes of -valent functions defined by multiplier transformations.
The radius of univalence and starlikeness of a certain class of analytic functions
The radius of univalence and starlikeness of some classes of regular functions
The radius of univalence of certain analytic functions
The Riemannian structure of John and uniform domains in .
The Riesz kernels do not give rise to higher dimensional analogues of the Menger-Melnikov curvature.
Ever since the discovery of the connection between the Menger-Melnikov curvature and the Cauchy kernel in the L2 norm, and its impressive utility in the analytic capacity problem, higher dimensional analogues have been coveted. The lesson from 1-sets was that any such (nontrivial, nonnegative) expression, using the Riesz kernels for m-sets in Rn, even in any Lk norm (k ∈ N), would probably carry nontrivial information on whether the boundedness of these kernels in the appropriate norm implies rectifiability...
The roots of a polynomial depend continuously on its coefficients.
The Schwarz-Christoffel conformal mapping for “polygons” with infinitely many sides.
The Schwarz-Christoffel conformal mapping for "polygons" with infinitely many sides.
The Schwarzian derivative and conformally natural quasiconformal extensions from one to two to three dimensions.
The Schwarzian derivative for conformal maps.
The Schwarz-Pick theorem and its applications
Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmén-Lindelöf principle, which is of course standard in such situations.
The second coefficient of a function with all derivatives univalent.
The sharp version of a criterion for starlikeness related to the operator of Alexander
The method of convolution is used to determine a sharp condition for starlikeness of analytic functions defined in the unit disc U = {z ∈ ℂ: |z| < 1} and having the property f(0) = f'(0) - 1 = 0. The integral version is given using the Alexander integral operator.
The smallest positive eigenvalue of a quasisymmetric automorphism of the unit circle
This paper provides sufficient conditions on a quasisymmetric automorphism γ of the unit circle which guarantee the existence of the smallest positive eigenvalue of γ. They are expressed by means of a regular quasiconformal Teichmüller self-mapping φ of the unit disc Δ. In particular, the norm of the generalized harmonic conjugation operator is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest positive eigenvalue...
The space of quasisymmetric mappings.
The starlikeness properties for integral operators.
The traveling salesman problem and harmonic analysis.
In this paper we propose to discuss some relationships between the classical Traveling Salesman Problem (TSP), Litlewood-Paley theory, and harmonic measure. This circle of ideas is also closely related to the theory of Cauchy integrals on Lipschitz graphs, and this aspect is discussed more fully in the paper of David and Semmes [2] in this proceedings. The main differences between the subjects in [2] and this paper are that the results here are valid for one dimensional sets, whereas [2] treats...