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

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Abstract

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.

Original languageEnglish
Pages (from-to)691-700
Number of pages10
JournalHouston Journal of Mathematics
Volume22
Issue number4
Publication statusPublished - 1996 Dec 1

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ASJC Scopus subject areas

  • Mathematics(all)

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