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.
Citation
Atsushi Atsuji. "Parabolicity, projective volume and finiteness of total curvature of minimal surfaces." Kodai Math. J. 27 (3) 227 - 236, October 2004. https://doi.org/10.2996/kmj/1104247348
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