On closed finite gap curves in spaceforms II

Abstract

We prove that the set of closed finite gap curves in hyperbolic 3-space ${\mathbb{H}}^3$ is $W^{2,2}$-dense in the Sobolev space of all closed $W^{2,2}$-curves in ${\mathbb{H}}^3$. We also show that the set of closed finite gap curves in any 2-dimensional space form ${\mathbb{E}}^2$ is $W^{2,2}$-dense in the Sobolev space of all closed $W^{2,2}$-curves in ${\mathbb{E}}^2$.

21 pages

References in corpus (1)

• On Closed Finite Gap Curves in Spaceforms I

Cited by in corpus (1)

• On Closed Finite Gap Curves in Spaceforms I