Minimal surfaces and $H$-surfaces in non-positively curved space forms

Positively Curved Surfaces in the Three-sphere

In this talk I will discuss an example of the use of fully nonlinear parabolic flows to prove geometric results. I will emphasise the fact that there is a wide variety of geometric parabolic equations to choose from, and to get the best results it can be very important to choose the best flow. I will illustrate this in the setting of surfaces in a three-dimensional sphere. There are quite a few...

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...

Minimal Surfaces in Euclidean Space

Minimal surfaces in H × R

We construct complete embedded minimal surfaces in H × R. The first one is a finite total curvature surface which is conformal to S \ {p1, ..., pk}, k ≥ 2; the second one is a 1-parameter family of singly-periodic minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the third one is a 2-parameter family of minimal surfaces which have a fundamental piece of finite tot...

Non-local Minimal Surfaces

In this paper we study the geometric properties, existence, regularity and related issues for a family of surfaces which are boundaries of sets minimizing certain integral norms. These surfaces can be interpreted as a non-infinitesimal version of classical minimal surfaces. Our work is motivated by the structure of interphases that arise in classical phase field models when very long space corr...