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تسجيل مستخدم جديدHarmonic measure and SLE
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In this paper we rigorously compute the average multifractal spectrum of harmonic measure on the boundary of SLE clusters.
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We give several new characterizations of Caratheodory convergence of simply connected domains. We then investigate how different definitions of convergence generalize to the multiply-connected case.
Let $E$ be a continuum in the closed unit disk $|z|le 1$ of the complex $z$-plane which divides the open disk $|z| < 1$ into $nge 2$ pairwise non-intersecting simply connected domains $D_k,$ such that each of the domains $D_k$ contains some point $a_
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We study a family of real rational functions with prescribed critical points and the evolution of its poles and critical points under particular Loewner flows. The recent work by Peltola and Wang shows that the real locus of these rational functions
contains the multiple SLE$(0)$ curves, the deterministic $kappa to 0$ limit of the multiple SLE$(kappa)$ system. Our main results highlight the importance of the poles of the rational function in determining properties of the SLE$(0)$ curves. We show that solutions to the classical limit of the the null vector equations, which are used in Loewner evolution of the multiple SLE$(0)$ curves, have simple expressions in terms of the critical points and the poles of the rational function. We also show that the evolution of the poles and critical points under the Loewner flow is a particular Calogero-Moser integrable system. A key step in our analysis is a new integral of motion for the deterministic Loewner flow.
Harmonic functions are natural generalizations of conformal mappings. In recent years, a lot of work have been done by some researchers who focus on harmonic starlike functions. In this paper, we aim to introduce two classes of harmonic univalent fun
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In the present paper, we will study geometric properties of harmonic mappings whose analytic and co-analytic parts are (shifted) generated functions of completely monotone sequences.
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