naa a22 4500 510810527 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s12220-011-9280-2 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9280-2 Neel Robert Department of Mathematics, Lehigh University, 14 East Packer Avenue, 18015, Bethlehem, PA, USA aut On Parabolicity and Area Growth of Minimal Surfaces [Elektronische Daten] [Robert Neel] We establish parabolicity and quadratic area growth for minimal surfaces-with-boundary contained in regions of ℝ3 which are within a sub-logarithmic factor of the exterior of a cone. Unlike previous work showing that these two properties hold for minimal surfaces-with-boundary contained between two catenoids, we do not make use of universal superharmonic functions. Instead, we use stochastic methods, which have the additional feature of giving a type of parabolicity in a more general context than Brownian motion on a minimal surface. Mathematica Josephina, Inc., 2011 Minimal surfaces nationallicence Parabolicity nationallicence Area growth nationallicence Brownian motion nationallicence Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1173-1188 1050-6926 23:3<1173 2013 23 12220 https://doi.org/10.1007/s12220-011-9280-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9280-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Neel Robert Department of Mathematics, Lehigh University, 14 East Packer Avenue, 18015, Bethlehem, PA, USA aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1173-1188 1050-6926 23:3<1173 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer