White's Compactness Theorem for Integral Currents
The Compactness Theorem is a
fundemental theorem of Geometric Measure Theory. In a sense, it
justifies for the theory itself, since it guarentees the existence of
minimal surfaces, thereby providing a solution to the extended problem
of Plateau. The original proof given by Federer and Fleming in the 60's
relied on their Structure Theorem. This is a fact that is hard to prove
and makes the compactness theorem rather difficult. Bruce Solomon
provided a solution which avoided the Structure Theorem in the mid
80's. However, Solomon's proof used multi-valued functions which have
their own setbacks. It was really Brian White's proof in 1987 which
made the Compactness Theorem approachable. In this thesis, I explore
this proof and justify many of the results which Brian has simply
"assumed." It is really in the hope that even a beginner to Geometric
Measure Theory maybe able to read this exposition and understand the
details of White's proof.
You can access it here: ctic.pdf
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