The least gradient (LG) flow, the total variation (TV) flow, and the
inverse mean curvature (IMC) flow arise in diverse applications from geometry
(nonparametric minimal surfaces), image processing (image denosing),
and the general relativity (isoperimetric inequality for black hole),
respectively. However, their mathematical descriptions and the
difficulties are closely related. This "close" relation can then
be exploited when comes to develop efficient numerical methods for
approximating these flows. In this talk, I will first describe the
"connection" between these flows, and then discuss some recent
developments on analysis and (finite element) numerical analysis of the
LG flow, the TV flow, and the IMC flow. Computation experiment results
will also be presented for the proposed numerical methods.
This is a joint work with Andreas Prohl of ETH Zurich, Switzerland.
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