201 citations · 424 across the 21 of their papers we have counts for
9 papers · 1 filter
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…
Coplanar constant mean curvature surfaces
Karsten Grosse-Brauckmann, Robert B. Kusner, John M. Sullivan
We consider constant mean curvature surfaces of finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were cons…
When Soap Bubbles Collide
Colin Adams, Frank Morgan, John M Sullivan
Can you fill R^n with a froth of "soap bubbles" that meet at most n at a time? Not if they have bounded diameter, as follows from Lebesgue's Covering Theorem. We provide some relat…
Some Ropelength-Critical Clasps
John M. Sullivan, Nancy C. Wrinkle
We describe several configurations of clasped ropes which are balanced and thus critical for the Gehring ropelength problem of arXiv:math.DG/0402212.