Deformations of complete minimal surfaces

Source abstract

A notion of deformation is defined and studied for complete minimal surfaces in R 3 {R^3} and R 3 / G , G {R^3}/G,G a group of translations. The catenoid, Enneper’s surface, and the surface of Meeks-Jorge, modelled on a 3 3 -punctured sphere, are shown to be isolated. Minimal surfaces of total curvature 4 π 4\pi in R 3 / Z {R^3}/Z and R 3 / Z 2 {R^3}/{Z^2} are studied. It is proved that the helicoid and Scherk’s surface are isolated under periodic perturbations.