On parabolicity and area growth of minimal surfaces
The paper establishes parabolicity and quadratic area growth for minimal surfaces-with-boundary contained in regions of \(\mathbb R^3\) which are within a sublogarithmic factor of the exterior of a cone. The author is interested in controlling the geometry and conformal structure of such surfaces under the assumption that they are contained in certain rotationally symmetric regions. The motivation for this comes in part from the fact that such surfaces arise as representatives of ends of complete minimal surfaces. No use is made of universal superharmonic functions. Instead, stochastic methods are used, which have the additional feature of giving a type of parabolicity in a more general context than Brownian motion on a minimal surface.
scientific article; zbMATH DE number 6203568