The Geometry and Conformal Structure of Properly Embedded Minimal Surfaces of Finite Topology in R

The topology, geometry and conformal structure of properly embedded minimal surfaces

Let M denote the set of connected properly embedded minimal surfaces in R with at least two ends. At the beginning of the past decade, there were two outstanding conjectures on the asymptotic geometry of the ends of an M ∈ M that were known to lead to topological restrictions on M . The first of these conjectures, the generalized Nitsche conjecture, stated that an annular end of such a M ∈ M is...

On the Existence of a Proper Minimal Surface in R with a Conformal Type of Disk

Proper minimal surfaces in R3 have peculiar properties that are not shared by general minimal surfaces; especially in the embedded case. It has been proved that, under additional conditions, this family of surfaces has strong restrictions on their conformal structures. For instance, Huber and Osserman proved that if M is a complete minimal surface with finite total curvature, then M has the con...

The influence of S-embedded subgroups on the structure of finite groups

Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite grou...

The Asymptotic Behavior of Properly Embedded Minimal Surfaces of Finite Topology

While advances have been made in recent years in the study of properly embedded minimal surfaces of finite topology in R3 [3,5,8,9, 11, 12, 13,23], progress has depended, in an essential manner, on the special structure of such surfaces with finite total curvature. A properly immersed minimal surface with finite total curvature is, conformally, a compact Riemann surface punctured in a finite nu...

The Geometry and Conformal Structure of ProperlyEmbedded Minimal Surfaces of Finite Topology inR 3