Macroscopic dimension of the $\ell^p$-ball with respect to the $\ell^q$-norm
We show estimates of the "macroscopic dimension" of the $\ell^p$-ball with respect to the $\ell^q$-norm.
math.MG↗
arXiv subjects
Masaki Tsukamoto
Publications and source records attributed to Masaki Tsukamoto.
Deformation of Brody curves and mean dimension
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 to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite dimensional. As an application we prove a lower bound on the mean dimension of the space of Brody curves.
math.DG↗
Moduli space of Brody curves, energy and mean dimension
We study the mean dimension of the moduli space of Brody curves. We introduce the notion of "mean energy" and show that this can be used to estimate the mean dimension.
math.DG↗
On holomorphic curves in algebraic torus
We study entire holomorphic curves in the algebraic torus, and show that they can be characterized by the ``growth rate'' of their derivatives.
math.CV↗
A packing problem for holomorphic curves
We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for holomorphic maps from elliptic curves to the complex projective space, and study the relation between theta functions and our packing problem. Applying the Nevanlinna theory, we investigate the packing densities of entire holomorphic curves in the complement of hyperplanes.
math.CV↗