Embedding and knotting of positive curvature surfaces in 3-space

In 3-space, compact orientable surfaces with nonempty boundary and positive curvature play the role of Seifert surfaces in a curvature-sensitive version of knot theory. The following result states that the isotopy classes of such surfaces are in a one-to-one correspondence with the isotopy classes of ordinary surfaces which have no constraint on their curvature.