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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