This textbook introduces geometric measure theory through the
notion of currents. Currents, continuous linear functionals on
spaces of differential forms, are a natural language in which to
formulate types of extremal problems arising in geometry, and can
be used to study generalized versions of the Plateau problem and
related questions in geometric analysis. Motivating key ideas with
examples and figures, this book is a comprehensive introduction
ideal for both self-study and for use in the classroom. The
exposition demands minimal background, is self-contained and
accessible, and thus is ideal for both graduate students and
researchers.
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