Related papers: A discrete Schwarzian derivative via circle packin…
The Wiener Sausage, the volume traced out by a sphere attached to a Brownian particle, is a classical problem in statistics and mathematical physics. Initially motivated by a range of field-theoretic, technical questions, we present a…
Quantitative estimates are obtained for the (finite) valence of functions analytic in the unit disk with Schwarzian derivative that is bounded or of slow growth. A harmonic mapping is shown to be uniformly locally univalent with respect to…
A discretisation of differential geometry using the Whitney forms of algebraic topology is consistently extended via the introduction of a pairing on the space of chains. This pairing of chains enables us to give a definition of the…
We describe the way in which the sign of the Schwarzian derivative for a family of diffeomorphisms of the interval $I$ affects the dynamics of an associated many-to-one skew product map of the cylinder $(\R/\Z)\times I$.
A decomposition of the Wiener measure based on its quasi-invariance under the group of diffeo- morphisms is proposed. As a result, functional integrals in the Schwarzian theory can be written as the Fourier transform of the integrals in a…
We formulate a strengthening of the Zariski dense orbit conjecture for birational maps of dynamical degree one. So, given a quasiprojective variety $X$ defined over an algebraically closed field $K$ of characteristic $0$, endowed with a…
\textit{Parastichies} are spiral patterns observed in plants and numerical patterns generated using golden angle method. We generalize this method by using Markoff theory and the theory of product of linear forms, to obtain a theory for…
We introduce the flower calculus, a deep inference proof system for intuitionistic first-order logic inspired by Peirce's existential graphs. It works as a rewriting system over inductive objects called ''flowers'', that enjoy both a…
We present the first steps of a procedure which discretises surface theory in classical projective differential geometry in such a manner that underlying integrable structure is preserved. We propose a canonical frame in terms of which the…
Attempts to build a discrete theory for rational maps on the sphere via circle packing have foundered on discretization effects in locating branch points. The authors remove this impediment by introducing generalized branch points. A…
From the geometric study of the elementary cell of hexagonal circle packings --- a flower of 7 circles --- the class of conformally symmetric circle packings is defined. Up to Moebius transformations, this class is a three parameter family,…
A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be…
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications but there is no systematic study of it. We present here a new technique, which…
In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that singular Schwartz distributions can be represented within that same…
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of…
We study families of analytic and meromorphic functions with bounded generalized Schwarzian derivative $S_k(f)$. We show that these families are quasi-normal. Further, we investigate associated families, such as those formed by derivatives…
The primary aim of this article is to extend certain inequalities concerning the pre-Schwarzian derivatives from the case of analytic univalent functions to that of univalent harmonic mappings defined on certain domains. This is done in two…
This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant…
In 1991, Beardon and Stephenson [2] generalized the classical Schwarz-Pick lemma in hyperbolic geometry to the discrete Schwarz-Pick lemma for Andreev circle packings. This paper continues to investigate the discrete Schwarz-Pick lemma for…
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…