SelectedWorks - Robert Kusner

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Selected Works of Robert Kusner

Professor, Department of Mathematics and Statistics, College of Natural Sciences

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About Robert Kusner

Present	Professor, Department of Mathematics and Statistics, College of Natural Sciences, University of Massachusetts Amherst
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Geometry and Topology

Geometric analysis and variational problems, low dimensional topology and geometry, mathematical visualization

Personal Webpage

Lederle Graduate Research Tower 1435G
University of Massachusetts Amherst
Amherst, MA 01003
Tel: 413-545-6022
Fax: 413-545-1801

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Unpublished Paper

The Expected Total Curvature of Random Polygons

American Journal of Mathematics (2015)

Jason Cantarella, Alexander Y. Grosberg, Robert Kusner and Clayton Shonkwiler

We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as ...

Unpublished Paper

Ropelength criticality

Geometry and Topology (2014)

Jason Cantarella, Joseph H.G. Fu, Robert B. Kusner and John M. Sullivan

The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve ...

Unpublished Paper

There is no triangulation of the torus with vertex degrees ...

Geometriae Dedicata (2012)

Ivan Izmestiev, Robert B. Kusner, Günter Rote, Boris Springborn, et al.

There is no 5,7-triangulation of the torus, that is, no triangulation with exactly two exceptional vertices, of degree 5 and ...

Unpublished Paper

Coplanar k-Unduloids Are Nondegenerate

International Mathematics Research Notices (2009)

Karsten Grosse-Brauckmann, Nicholas J. Korevaar, Robert Kusner, Jesse Ratzkin, et al.

We prove each embedded, constant mean curvature (CMC) surface in Euclidean space with genus zero and finitely many coplanar ends ...

Coplanar Constant Mean Curvature Surfaces

Communications in Analysis and Geometry (2007)

Karsten Grosse-Brauckmann, Robert Kusner and John M. Sullivan

We consider constant mean curvature surfaces with finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces ...

Unpublished Paper

Criticality for the Gehring link problem

Geometry & Topology (2006)

Jason Cantarella, Joseph H.G. Fu, Robert Kusner, John M. Sullivan, et al.

In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint ...

Unpublished Paper

On the Nondegeneracy of Constant Mean Curvature Surfaces

Geometric And Functional Analysis (2006)

Nick Korevaar, Robert Kusner and Jesse Ratzkin

We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:\Sigma \to \R^3$ are nondegenerate; that is, the Jacobi ...

Conformal Structures And Necksizes Of Embedded Constant Mean Curvature Surfaces

Mathematical Sciences Research Institute (2005)

Let M = M_{g,k} denote the space of properly (Alexandrov) embedded constant mean curvature (CMC) surfaces of genus g with ...

Unpublished Paper

The topology, geometry and conformal structure of properly embedded minimal ...

Journal of Differential Geometry (2004)

Pascal Collin, Robert Kusner, William H. Meeks and Harold Rosenberg

This paper develops new tools for understanding surfaces with more than one end and infinite topology which are properly minimally ...

Unpublished Paper

The Second Hull of a Knotted Curve

American Journal of Mathematics (2003)

Jason Cantarella, Greg Kuperberg, Robert B. Kusner and John M. Sullivan

The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by ...

Unpublished Paper

On the Minimum Ropelength of Knots and Links

Inventiones mathematicae (2002)

Jason Cantarella, Robert B. Kusner and John M. Sullivan

The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded ...

On Thickness and Packing Density for Knots and Links

Contemporary Mathematics (2002)

We describe some problems, observations, and conjectures concerning density of the hexagonal packing of unit disks in R2.thickness and packing ...

Unpublished Paper

Constant Mean Curvature Surfaces With Three Ends

Proceedings of the National Academy of Sciences of the United States of America (2000)

Karsten Grosse-Brauckmann, Robert Kusner and John M. Sullivan

We announce the classification of complete almost embedded surfaces of constant mean curvature, with three ends and genus zero. They ...

Triunduloids: Embedded Constant Mean Curvature Surfaces With Three Ends and ...

Proceedings of the National Academy of Sciences (2000)

Karsten Grosse-Brauckmann, Robert Kusner and John M. Sullivan

We announce the classification of complete almost embedded surfaces of constant mean curvature, with three ends and genus zero. They ...

Unpublished Paper

On Distortion And Thickness Of Knots

IMA Volumes in Mathematics and Its Applications (1998)

Robert B. Kusner and John M. Sullivan

What length of rope (of given diameter) is required to tie a particular knot? Or, to turn the problem around, ...

Unpublished Paper

Moduli Spaces Of Embedded Constant Mean Curvature Surfaces With Few ...

Karsten Grosse-Brauckmann and Robert Kusner

We give necessary conditions on complete embedded cmc surfaces with three or four ends subject to reflection symmetries. The respective ...

Unpublished Paper

The Moduli Space Of Complete Embedded Constant Mean Curvature Surfaces

Geometric & Functional Analysis (1996)

Robert Kusner, Rafe Mazzeo and Daniel Pollack

We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These ...

Unpublished Paper

The Spinor Representation of Surfaces in Space

Robert Kusner and Nick Schmitt

The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan ...