相关论文: Moduli space of Brody curves, energy and mean dime…

We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.

Mean dimension measures the size of an infinite dimensional dynamical system. Brody curves are one-Lipschitz entire holomorphic curves in the projective space, and they form a topological dynamical system. Gromov started the problem of…

We introduce several definitions of energy density of Brody curves and show that they give the same value in an appropriate situation.

We study the mean dimension of the space of 1-Brody curves lying in two complex surfaces: first for Hopf surfaces, then for the projective plane minus a line. We show in the first case that the mean dimension is zero via a bound on the…

The main purpose of this paper is to show that ideas of deformation theory can be applied to "infinite dimensional geometry". We develop the deformation theory of Brody curves. Brody curve is a kind of holomorphic map from the complex plane…

We give a formula to compute the dimension of the generic component of the moduli space of an irreducible germ of curve in the complex plane.

We first partially extend a theorem of Topping, on the relation between mean curvature and intrinsic diameter, from immersed submanifolds of $\mathbb{R} ^{n} $ to almost everywhere immersed, closed submanifolds of a compact Riemannian…

Polygon spaces have been studied extensively, and yet missing from the literature is a simple property that every polygon has: dimension. This is distinct (possibly) from the dimension of the ambient space in which the polygon lives. A…

We explicitly compute the moduli space pointed algebraic curves with a given numerical semigroup as Weierstrass semigroup for many cases of genus at most seven and determine the dimension for all semigroups of genus seven.

This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…

This paper studies the moduli space of stable surfaces of general type. The moduli space component containing the moduli point of a product of smooth curves of general type is proved to be the product of the moduli spaces of the curves,…

We sharpen our previous results on the g and n such that the moduli space of curves of genus g with n marked points is of general type.

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

We find upper bounds for the essential dimension of various moduli stacks of $\sln$-bundles over a curve. When $n$ is a prime power, our calculation computes the essential dimension of the stack of stable bundles exactly and the essential…

We review the following subjects: 1. Basic theory on algebraic curves and their moduli space, 2. Schottky uniformization theory of Riemann surfaces, and its extension called arithmetic uniformization theory, 3. Application to these theories…

We investigate Brody curves in the projective space from the point of view of Nevanlinna theory.

We present an explicit method to produce upper bounds for the dimension of the moduli spaces of complete integral Gorenstein curves with prescribed symmetric Weierstrass semigroups.

A well-known principle of Mumford asserts that all moduli spaces of curves are varieties of general type, except a finite number of cases that occur for relatively small genus, when these varieties tend to be uniruled. In all known cases,…

The main purpose of this paper is to propose an ergodic theoretic approach to the study of entire holomorphic curves. Brody curves are one-Lipschitz holomorphic maps from the complex plane to the complex projective space. They naturally…

We define and study a M\"obius invariant energy associated to planar domains, as well its generalization to space curves. This generalization is a M\"obius version of Banchoff-Pohl's notion of area enclosed by a space curve. A relation with…