328 citations · 682 across the 29 of their papers we have counts for
19 papers · 1 filter
Nonorientable Minimal Surfaces Embedded in the Round -sphere
Mikhail Karpukhin, Robert Kusner, Peter McGrath +1
We show that every closed, nonorientable surface can be minimally embedded in , providing in particular the first known examples of embedded, nonorientable minimal su…
The Willmore problem for surfaces with symmetry
Rob Kusner, Ying Lü, Peng Wang
The Willmore Problem seeks closed surfaces in of a given topological type minimizing the squared-mean-curvature energy $W = \int |H_{\mathbb{R}^4}…
Embedded minimal surfaces in and via equivariant eigenvalue optimization
Mikhail Karpukhin, Robert Kusner, Peter McGrath +1
In 1970, Lawson solved the topological realization problem for minimal surfaces in the sphere, showing that any closed orientable surface can be minimally embedded in $\mathbb{S}^3…
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions
Jonas Hirsch, Rob Kusner, Elena Mäder-Baumdicker
We study complete minimal surfaces in with finite total curvature and embedded planar ends. After conformal compactification via inversion, these yield examples of s…
On the Canham Problem: Bending Energy Minimizers for any Genus and Isoperimetric Ratio
Robert Kusner, Peter McGrath
Building on work of Mondino-Scharrer, we show that among closed, smoothly embedded surfaces in of genus and given isoperimetric ratio , there exists one with…
On the Willmore problem for surfaces with symmetry
Rob Kusner, Peng Wang
The Willmore Problem seeks the surface in of a given topological type minimizing the squared-mean-curvature energy $W = \int |\mathbf{H}_{\mathbb{R}…
On Steklov Eigenspaces for Free Boundary Minimal Surfaces in the Unit Ball
Robert Kusner, Peter McGrath
We develop new methods to compare the span of the coordinate functions on a free boundary minimal submanifold embedded in the unit -ball with…
On the index of minimal 2-tori in the 4-sphere
Rob Kusner, Peng Wang
In this note we prove that any minimal -torus in has Morse index at least , with equality if and only if it is congruent to the Clifford torus in some great $S^3\subset…
The Expected Total Curvature of Random Polygons
Jason Cantarella, Alexander Y Grosberg, Robert B. Kusner +1
We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference be…
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…
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…
On the nondegeneracy of constant mean curvature surfaces
Nick Korevaar, Rob Kusner, Jesse Ratzkin
We prove that many complete, noncompact, constant mean curvature (CMC) surfaces are nondegenerate; that is, the Jacobi operator has no kernel. I…
Criticality for the Gehring link problem
Jason Cantarella, Joseph H G Fu, Rob Kusner +2
In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and…
The topology, geometry and conformal structure of properly embedded minimal surfaces
Pascal Collin, Robert Kusner, William H. Meeks +2
This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On su…
Conformal Structures and Necksizes of Embedded Constant Mean Curvature Surfaces
Rob Kusner
Let M = M_{g,k} denote the space of properly (Alexandrov) embedded constant mean curvature (CMC) surfaces of genus g with k (labeled) ends, modulo rigid motions, endowed with the r…
On Thickness and Packing Density for Knots and Links
Rob Kusner
We describe some problems, observations, and conjectures concerning thickness and packing density of knots and links in $\sp^3$ and . We prove the thickness of a nontrivial k…
Triunduloids: Embedded constant mean curvature surfaces with three ends and genus zero
Karsten Grosse-Brauckmann, Robert B Kusner, John M Sullivan
In 1841, Delaunay constructed the embedded surfaces of revolution with constant mean curvature (CMC); these unduloids have genus zero and are now known to be the only embedded CMC…
Constant mean curvature surfaces with three ends
Karsten Grosse-Brauckmann, Robert B. Kusner, John M. Sullivan
We announce the classification of complete, almost embedded surfaces of constant mean curvature, with three ends and genus zero: they are classified by triples of points on the sph…