Immersions of Finite Geometric Type in Euclidean Spaces

Abstract

In this paper, we introduce the class of hypersurfaces of finitegeometric type. They are defined as the ones that share the basicdifferential topological properties of minimal surfaces of finite totalcurvature. We extend to surfaces in this class the classical theorem ofOsserman on the number of omitted points of the Gauss mapping ofcomplete minimal surfaces of finite total curvature. We give aclassification of the even-dimensional catenoids as the only even-dimensional minimal hypersurfaces of R n of finite geometric type.