Valence and oscillation of functions in the unit disk.
Variability regions of close-to-convex functions
M. Biernacki gave in 1936 concrete forms of the variability regions of z/f(z) and zf'(z)/f(z) of close-to-convex functions f for a fixed z with |z|<1. The forms are, however, not necessarily convenient to determine the shape of the full variability region of zf'(z)/f(z) over all close-to-convex functions f and all points z with |z|<1. We propose a couple of other forms of the variability regions and see that the full variability region of zf'(z)/f(z) is indeed the complex plane minus the origin....
Variability sets on Riemann surfaces and forgetful maps between Teichmüller spaces.
Varianten des Schwarzschen Lemma.
Variation of quasiconformal mappings on lines
We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.
Variations of Robin capacity and applications.
Vector fields on the space of functions univalent inside the unit disk via Faber polynomials.
Velocity induced by a plane uniform vortex having the Schwarz function of its boundary with two simple poles.
Verallgemeinerung eines Bieberbachschen Satzes.
Verification of Brannan and Clunie's conjecture for certain subclasses of bi-univalent functions
Let σ denote the class of bi-univalent functions f, that is, both f(z) = z + a₂z² + ⋯ and its inverse are analytic and univalent on the unit disk. We consider the classes of strongly bi-close-to-convex functions of order α and of bi-close-to-convex functions of order β, which turn out to be subclasses of σ. We obtain upper bounds for |a₂| and |a₃| for those classes. Moreover, we verify Brannan and Clunie’s conjecture |a₂| ≤ √2 for some of our classes. In addition, we obtain the Fekete-Szegö relation...
Versions of Koebe 1/4 Theorem for Analytic and Quasiregular Harmonic Functions and Applications
Verzerrungsaussagen bei quasikonformen Abbildungen mit ortsabhängiger Dilationsbeschränkung und ein Extremalprinzip der Elektrostatik in inhomogenen Medien.
Voisinages connexes des points de Misiurewicz
On montre que tout point de Misiurewicz dans l’ensemble de Mandelbrot possède un système fondamental de voisinages connexes dans .
Volterra-type operators on Zygmund spaces.