Kodai Mathematical Journal

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

Atsushi Atsuji

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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.

Article information

Source
Kodai Math. J., Volume 27, Number 3 (2004), 227-236.

Dates
First available in Project Euclid: 28 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1104247348

Digital Object Identifier
doi:10.2996/kmj/1104247348

Mathematical Reviews number (MathSciNet)
MR2100920

Zentralblatt MATH identifier
1093.53008

Citation

Atsuji, Atsushi. Parabolicity, projective volume and finiteness of total curvature of minimal surfaces. Kodai Math. J. 27 (2004), no. 3, 227--236. doi:10.2996/kmj/1104247348. https://projecteuclid.org/euclid.kmj/1104247348


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