About a family of deformations of the Costa-Hoffman-Meeks surfaces

Abstract

We show the existence of a family of minimal surfaces obtained by deformations of the Costa-Hoffman-Meeks surface of genus k a (c) 3/4 1, M (k) . These surfaces are obtained varying the logarithmic growths of the ends and the directions of the axes of revolution of the catenoidal type ends of M (k) . Also we obtain a result about the non degeneracy property of the surface M (k) .