On the number of the minimal surfaces spanning part of a knot

In this paper we will consider the number of minimal surfaces which do not touch all of a C³ knot in R³. We find a lower bound of the number of soap-film-like minimal surfaces spanning part of a given C³ knot in R³. This lower bound is called the admissible number of the knot. To do this, we will use the model defined by H.R. Parks [4], soap-film-like minimal suraces homotopically spanning knots modulo L.