Research Papers:

Globalizing two-dimensional unstable manifolds of maps

by Bernd Krauskopf and Hinke Osinga

This electronic document presents an algorithm for computing the global two-dimensional unstable manifold of a normally hyperbolic invariant circle of a three-dimensional map. The algorithm computes intersections of the unstable manifold with a finite number of leaves of a chosen linear foliation. This makes is possible to guarantee the quality of the mesh on this manifold.

A Tight Polyhedral Immersion of the Real Projective Plane with one Handle

by Davide P. Cervone.

This multimedia paper describes a newly discovered tight polyhedral immersion of the non-orientable surface of Euler characteristic -1. The existence of this surface is surprising, since it has been proven that no smooth tight immersion of this surface is possible.

Interactive Methods for Visualizable Geometry

by Andrew J. Hanson, Tamara Munzner, and George Francis.

Interactive computer graphics methods provide new insights into the world of pure geometry. This paper describes some recent attempts to use computer graphics to understand deep problems in modern mathematics.

Visualizing the Structure of the World Wide Web in 3D Hyperbolic Space

by Tamara Munzner and Paul Burchard.

The World-Wide Web has so many interconnections that it is difficult to visualize even a small part of it using conventional graphs. This paper introduces a visualization technique that use hyperbolic space and the WebOOGL software developed at the Geometry Center for an innovative solution to this problem.

Some planar isospectral domains

by Peter Buser, John Conway, Peter Doyle, and Klaus-Dieter Semmler.

This paper answers the question, ``Can you hear the shape of a drum?''

Homotopy Hyperbolic 3-Manifolds Are Hyperbolic

by David Gabai, G. Robert Meyerhoff, and Nathaniel Thurston.

This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This technique is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold.

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Created: Jan 26 1995 --- Last modified: Thu Sep 11 16:34:41 1997