Ends of negatively curved surfaces in Euclidean space

We examine the geometry of a complete, negatively curved surface isometrically embedded in ${mathbb{R}^3}$ . We are especially interested in the behavior of the ends of the surface and its limit set at infinity. Various constructions are developed, and a classification theorem is obtained, showing that every possible end type for a topologically finite surface with at least one bowl end arises, as well as all infinite type surfaces with a single nonannular end. Some other examples are given with oddly behaved bowl ends.