2007/12/03 by Masaki Tsukamoto, Tsukamoto, Masaki
Mathematics · #32H30 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.0712.0266
openalex publication_date 2007/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.