Related papers: Continuous LERW Started from Interior Points

The classical Brouwer fixed point theorem states that in R^d every continuous function from a convex, compact set on itself has a fixed point. For an arbitrary probability space, let L^0 = L^0 (\Omega, A,P) be the set of random variables.…

We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle given in terms of the exponential of Gaussian Free Field. We conjecture that our curves are locally…

The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in $\mathbb C^2$. Our class is self-dual; it contains some domains with less than $C^2$-smooth boundary and also some domains with smooth…

We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the…

Among diversity of frameworks and constructions introduced in Loewner Theory by different authors, one can distinguish two closely related but still different ways of reasoning, which colloquially may be described as "increasing" and…

In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $\Bbb R^2.$ The classification gives…

A behavior of homeomorphisms of Orlicz classes in a closure of a domain is investigated. It is proved that above classes are equicontinuous in the closure of domains with some restrictions on it's boundaries provided that the corresponding…

For some class of mappings satisfying upper modular estimates with respect to families of curves, a behavior of the corresponding inverse mappings is investigated. In the terms of prime ends, it is proved that, families of such…

We study local connectedness, local accessibility and finite connectedness at the boundary, in relation to the compactness of the Mazurkiewicz completion of a bounded domain in a metric space. For countably connected planar domains we…

In this paper, we discuss the chordal Komatu-Loewner equation on standard slit domains in a manner applicable not just to a simple curve but also a family of continuously growing hulls. Especially a conformally invariant characterization of…

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…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…

The fundamental problem of calculus of variations is considered when solutions are differentiable curves on locally convex spaces. Such problems admit an extension of the Euler-Lagrange equations [Orlov 2002] for continuously normally…

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…

We show that the nonlinear 2+1--dimensional Three--Wave Resonant Interaction equations, describing several important physical phenomena, can be generated starting from incomplete Lie algebras in the framework of multidimensional…

This paper provides an overview of Lawvere's Fixed-Point Theorem in category theory and aims to detail the universal framework underlying self-reference and recursive structures. First, we rigorously define fundamental concepts - such as…

We generate hierarchies of derivative nonlinear Schr\"odinger-type equations and their nonlocal extensions from Lie algebra splittings and automorphisms. This provides an algebraic explanation of some known reductions and newly established…

We apply parallel approaches in the study of continuous spectra to adiabatic stellar models. We seek continuum eigenmodes for the LAWE formulated as both finite difference and linear differential equations. In particular, we apply methods…

We present basic properties of Dipolar SLEs, a new version of stochastic Loewner evolutions (SLE) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We present a general argument explaining why…

We study the possibility of a continuous extension of a class of mappings to an isolated point on the boundary of a domain. We show that if some characteristic of this mapping is integrable on almost all spheres in the neighborhood of at…