Index and Flat Ends of Minimal Surfaces

On helicoidal ends of minimal surfaces

Digital cohomology groups of certain minimal surfaces

In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital sph...

Critical Heegaard Surfaces and Index 2 Minimal Surfaces

This paper contains the motivation for the study of critical surfaces in [2]. In that paper, the only justification given for the definition of this new class of surfaces is the strength of the results. However, when viewed as the topological analogue to index 2 minimal surfaces, critical surfaces become quite natural.

On Singly-periodic Minimal Surfaces with Planar Ends

The spaces of nondegenerate properly embedded minimal surfaces in quotients of R3 by nontrivial translations or by screw motions with nontrivial rotational part, fixed finite topology and planar type ends, are endowed with natural structures of finite dimensional real analytic manifolds. This nondegeneracy is defined in terms of Jacobi functions. Riemann’s minimal examples are characterized as ...

On Properly Embedded Minimal Surfaces with Three Ends

We classify all complete embedded minimal surfaces in R3 with three ends of genus g and at least 2g + 2 symmetries. The surfaces in this class are the Costa-HoffmanMeeks surfaces that have 4g + 4 symmetries in the case of a flat middle end. The proof consists of using the symmetry assumptions to deduce the possible Weierstrass data and then studying the period problems in all cases. To handle t...