201 citations · 424 across the 21 of their papers we have counts for
21 papers
Classification of small links in the unmarked solid torus
John M. Sullivan, Max Zahoransky von Worlik
We introduce a framework to analyze knots and links in an unmarked solid torus. We discuss invariants that detect when such links are equivalent under an ambient homeomorphism, and…
Ropelength Criticality
Jason Cantarella, Joseph H. G. Fu, Robert Kusner +1
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight k…
Coplanar k-unduloids are nondegenerate
Karsten Grosse-Brauckmann, Nicholas J. Korevaar, Robert B. Kusner +2
We prove each embedded, constant mean curvature (CMC) surface in Euclidean space with genus zero and finitely many coplanar ends is nondegenerate: there is no nontrivial square-int…
Curvatures of Smooth and Discrete Surfaces
John M. Sullivan
We discuss notions of Gauss curvature and mean curvature for polyhedral surfaces. The discretizations are guided by the principle of preserving integral relations for curvatures, l…
Convergence and isotopy type for graphs of finite total curvature
Elizabeth Denne, John M Sullivan
Generalizing Milnor's result that an FTC (finite total curvature) knot has an isotopic inscribed polygon, we show that any two nearby knotted FTC graphs are isotopic by a small iso…
Curves of Finite Total Curvature
John M Sullivan
We consider the class of curves of finite total curvature, as introduced by Milnor. This is a natural class for variational problems and geometric knot theory, and since it include…