The Reduction of Two Dimensional Integrals into a Finite Number of One Dimensional Integrals
The remainder term of the Taylor expansion for a holomorphic function is representable in Lagrange form.
The return sequence of the Bowen-Series map for punctured surfaces
For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the Liouville measure. ...
The Riemann surface of a uniform dessin.
The Riemannian structure of John and uniform domains in .
The Riemann-Roch theorem and geometry, 1854-1914.
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 Second Homology Group of the Mapping Class Group of an Orientable Surface.
The second main theorem for algebroid functions.
The Serre duality theorem for Riemann surfaces.
The Serre Problem on Riemann Surfaces.
The set of Lindelöf points for meromorphic functions
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.