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The purpose of this note is to show how certain ideas from dynamical systems theory can be generalised to nonlinear elliptic PDE.

This is the first of a two-part paper in which we develop a theory of parabolic equations for curves on surfaces which can be applied to the so-called curve shortening of flow-by-mean-curvature… (More)

If (M 2,g) is a surface with Riemannian metric, then a family of immersed curves C t | 0 ≤ t < T on M 2 evolves by Curve Shortening if where K g is the geodesic curvature, and v is a unit normal to… (More)

Abstract We define a “renormalized” Morse index, and prove a Bahri–Lions type result for critical points of E(u,v)= ∫ Ω {∇u·∇v−H(x,u,v)} d x ; i.e., we establish an a priori bound for critical points… (More)

Many nonlinear parabolic equations in Geometry and Applied Mathematics (mean curvature flow, Ricci flow, harmonic map flow, the Yang-Mills flow, reaction diffusion equations such as ut = ∆u + u )… (More)

- Sigurd B. Angenent, Eric Pichon, Allen R. Tannenbaum
- Bulletin (new series) of the American…
- 2006

In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based… (More)

- Ayelet Dominitz, Sigurd B. Angenent, Allen R. Tannenbaum
- Recent Advances in Learning and Control
- 2008

The optimal mass transport methodology has numerous applications in econometrics, fluid dynamics, automatic control, statistical physics, shape optimization, expert systems, and meteorology. Further,… (More)

- Steven Haker, Sigurd B. Angenent, Allen R. Tannenbaum, Ron Kikinis
- Medical Imaging
- 2000

In this paper, we propose a new 3D visualization technique for virtual colonoscopy. Such visualization methods could have a major impact since they have the potential for non-invasively determining… (More)

In the above paper (see S. Haker et al., ibid., vol.19, p.665-70, 2000), Figs. 2-5 should have appeared in color as shown here.