The numerical considerations involved with successfully simulating a
deforming manifold can be especially challenging. The first step in
this process is to choose a way to represent the manifold. The
strategies and techniques available diverge from this point on,
leading to different advantages and disadvantages in the resulting
algorithm. We investigate in this talk the choice of the implicit
representation using the level set method, with the goal of introducing
some advances and detailing the procedures involved with the framework.
To achieve this, we will cover details of the level set method applied to
the Minkowski problem as well as flows arising from Poisson-type problems
and representations of higher codimensional objects.
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