Compact complete null curves in complex 3-space

摘要

We prove that for any open orientable surface S of finite topology, there exist a Riemann surface M, a relatively compact domain M ⊂ M and a continuous map X: (overline M ) → ℂ3 such that: M and M are homeomorphic to S, M-M and M − (overline M ) contain no relatively compact components in M