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math.GT2005
Morse field theory
Ralph L. Cohen, Paul Norbury
In this paper we define and study the moduli space of metric-graph-flows in a manifold M. This is a space of smooth maps from a finite graph to M, which, when restricted to each ed…
math.GT2003
Closed geodesics on incomplete surfaces
Paul Norbury, J. Hyam Rubinstein
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening meth…
math.GT2002
Minimal spheres of arbitrarily high Morse index
Joel Hass, Paul Norbury, J. Hyam Rubinstein
We construct a smooth Riemannian metric on any 3-manifold with the property that there are genus zero embedded minimal surfaces of arbitrarily high Morse index.