相关论文: Topological characterisations of Loewner traces

Suppose X is a (smooth projective irreducible algebraic) curve over a finite field k. Counting the number of points on X over all finite field extensions of k will not determine the curve uniquely. Actually, a famous theorem of Tate implies…

For functions from the Sobolev space $H^s(\Omega)$, 1/2<s<3/2, definitions of non-unique generalised and unique canonical co-normal derivative are considered, which are related to possible extensions of a partial differential operator and…

We study the normal map for plane projective curves, i.e., the map associating to every regular point of the curve the normal line at the point in the dual space. We first observe that the normal map is always birational and then we use…

We give a criterion when a planar tree-like curve, i.e. a generic immersed plane curve each double point of which cuts it into two disjoint parts, can be send by a diffeomorphism of the plane onto a curve with no inflection points. We also…

We show that a general canonical curve is uniquely determined by the finite set of hyperplanes cutting theta-characteristics on it. Geometrical and combinatorial properties of the moduli space of stable spin curves are proved, which play an…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

Using concepts of noncommutative probability we show that the Loewner's evolution equation can be viewed as providing a map from paths of measures to paths of probability measures. We show that the fixed point of the Loewner map is the…

The traces of gauge-covariant Sobolev spaces on a Riemannian vector bundle for some connection are characterised as some gauge-covariant fractional Sobolev spaces when the curvature of the connection is bounded. The constants in the trace…

In this paper, we discuss the trace operator for homogeneous fractional Sobolev spaces over infinite strip-like domains. We determine intrinsic seminorms on the trace space that allow for a bounded right inverse. The intrinsic seminorm…

In this paper, we define and study Loewner chains and evolution families on finitely multiply-connected domains in the complex plane. These chains and families consist of conformal mappings on parallel slit half-planes and have one and two…

In complex systems with fractal properties the scale invariance has an important rule to classify different statistical properties. In two dimensions the Loewner equation can classify all the fractal curves. Using the Weierstrass-Mandelbrot…

We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the intuitive ideas that lead to the definition…

Can the cross product be generalized? Why are the trace and determinant so important in matrix theory? What do all the coefficients of the characteristic polynomial represent? This paper describes a technique for `doodling' equations from…

We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…

Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer…

A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…

Schramm-Loewner Evolutions (SLEs) describe a one-parameter family of growth processes in the plane that have particular conformal invariance properties. For instance, SLE can define simple random curves in a simply connected domain. In this…

We consider unbounded curves without endpoints. Isomorphism is equivalence up to translation. Self-avoiding plane-filling curves cannot be periodic, but they can satisfy the local isomorphism property: We obtain a set $\Omega $ of coverings…

Nonnegative measures that are solutions to a transport equation with continuous coefficients have been widely studied. Because of the low regularity of the associated vector field, there is no natural flow since nonuniqueness of integral…

The Stochastic Loewner equation, introduced by Schramm, gives us a powerful way to study and classify critical random curves and interfaces in two-dimensional statistical mechanics. New kind of stochastic Loewner equation, called fractional…