相关论文: On driving functions generating quasislits in the …
A quasislit is the image of a vertical line segment [0, iy], y > 0, under a quasiconformal homeomorphism of the upper half-plane fixing infinity. Quasislits correspond precisely to curves generated by the Loewner equation with a driving…
We consider the chordal Loewner differential equation for multiple slits in the upper half-plane and relations between the pointwise H\"older continuity of the driving functions and the generated hulls. The first result generalizes a result…
We obtain a first order differential equation for the driving function of the chordal Loewner differential equation in the case where the domain is slit by a curve which is a trajectory arc of certain quadratic differentials. In particular…
We consider the Loewner differential equation generating univalent maps of the unit disk (or of the upper half-plane) onto itself minus a single slit. We prove that the circular slits, tangent to the real axis are generated by H\"older…
In this paper, we show that the chordal Loewner differential equation with $C^{\beta}$ driving function generates a $C^{\beta + 1/2}$ slit for $1/2 < \beta \leq 2$, except when $\beta = 3/2$ the slit is only proved to be weakly $C^{1,1}$.
In part 1 (Chapter 2) we present the basic notions of Loewner theory. Here we use a modern form which was developed by F. Bracci, M. Contreras, S. D\'iaz-Madrigal et al. and which can be applied to certain higher dimensional complex…
We consider the L\"owner differential equation generating univalent self-maps of the unit disk (or of the upper half-plane). If the solution to this equation represents a one-slit map, then the driving term is a continuous function. The…
We study the chordal Loewner equation associated with certain driving functions that produce infinitely many slits. Specifically, for a choice of a sequence of positive numbers $(b_n)_{n\ge1}$ and points of the real line $(k_n)_{n\ge1}$, we…
In paper found conditions that guarantee that solution of Loewner-Kufarev equation maps unit disc onto domain with quasiconformal rectifiable boundary, or it has continuation on closed unit disc, or it's inverse function has continuation on…
We derive the variational formula of the Loewner driving function of a simple chord under infinitesimal quasiconformal deformations with Beltrami coefficients supported away from the chord. As an application, we obtain the first variation…
We consider the Hastings--Levitov HL(0) model in the small particle scaling limit and prove a large deviation principle. The rate function is given by the relative entropy of the driving measure $\rho$ for the Loewner--Kufarev equation: \[…
D. Marshall and S. Rohde have recently shown that there exists $C_0 >0$ so that the Loewner equation generates slits whenever the driving term is H\"older continuous with exponent 1/2 and norm less than $C_0$. In this paper, we show that…
Consider the Loewner equation associated to the upper-half plane. Normally this equation is driven by a real-valued function. In this paper, we show that when the driving function is complex-valued with small $1/2$-H\"older norm, the…
The limit functions generated by quasi-linear functions or sequences (including the sum of the Rudin-Shapiro sequence as an example) are continuous but almost everywhere non-differentiable functions. Their graphs are fractal curves. In 2017…
We show that, for $0<s<1$, $0<p<\infty$, $0<q<\infty$, Haj\l asz-Besov and Haj\l asz-Triebel-Lizorkin functions can be approximated in the norm by discrete median convolutions. This allows us to show that, for these functions, the limit of…
By considering a certain univalent function in the open unit disk U, that maps U onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential…
The paper is devoted to the multiple chordal Loewner differential equation with different driving functions on two time intervals. We obtain exact implicit or explicit solutions to the Loewner equations with piecewise constant driving…
Let $\lambda:[0,+\infty)\mapsto\mathbb{R}$ be the driving function of a chordal Loewner process. In this paper we find new conditions on $\lambda$ which imply that the process is generated by a simple curve. This result improves former one…
We analyze Loewner traces driven by functions asymptotic to K\sqrt{1-t}. We prove a stability result when K is not 4 and show that K=4 can lead to non locally connected hulls. As a consequence, we obtain a driving term \lambda(t) so that…
We show that, under mild assumptions on the limiting curve, a sequence of simple chordal planar curves converges uniformly whenever certain Loewner driving functions converge. We extend this result to random curves. The random version…