COMPLETE MINIMAL CYLINDERS PROPERLY IMMERSED IN THE UNIT BALL

Abstract

The Calabi-Yau conjecture is one of the main problems in the global theory of complete minimal surfaces in R³. Francisco Martin and Santiago Morales have constructed complete proper minimal surfaces in convex bodies of R³. In this paper, we modify their technique in the cylindrical case, and construct a complete minimal cylinder properly immersed in the unit ball.