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

[摘要] References(15)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.

[学科分类] 数学（综合）

[关键词] Minimal surface;Brownian motion;Nevanlinna theory