A packing problem for holomorphic curves

Details A packing problem for holomorphic curves A packing problem for holomorphic curves

2006-05-13

arxiv.org/abs/math/0605353v1

Mathematics

Complex Variables

33 pages

Scientific paper

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.

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