Scientists probe geometric conundrums
Researchers from Koç University in Turkey are investigating five problems in the fields of geometric topology and differential geometry. While some of the problems have puzzled scientists for years, and any partial results would be an important contribution to the fields, the others are bang up-to-date, and close to current interests. Working under the aegis of the 'Minimal surfaces in 3-manifolds' (MSI3M) project, scientists will examine the five problems in minimal surface theory in hyperbolic space using topological techniques. The problems are the embedded plateau problem, the hyperbolic three-manifolds with minimal foliation issue, the universal cover problem, the intersections of least area planes in hyperbolic space question and the problem known as 'properly embedded least area planes in hyperbolic three-space'. The scientists said that in the first two years of the project, they have gained 'substantial results' on several of the problems. However, problem three, the so-called 'properly embedded least area planes in hyperbolic three-space' and 'one of the oldest problems in three-manifold topology' is causing the researchers greater difficulties. 'We are still working on this problem and there is a good progress so far,' they commented.
