Parabolicity, projective volume and finiteness of total curvature of minimal surfaces

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Abstract

We show that finiteness of a projective volume implies finiteness of total curvature for stochastic complete minimal surfaces with finite number of ends and finite genus which may not be geodesically complete. The tools we use include simple stochastic calculus and Nevanlinna theoretic method.

Original languageEnglish
Pages (from-to)227-236
Number of pages10
JournalKodai Mathematical Journal
Volume27
Issue number3
DOIs
Publication statusPublished - 2004 Jan 1

Keywords

  • Brownian motion
  • Minimal surface
  • Nevanlinna theory

ASJC Scopus subject areas

  • Mathematics(all)

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