Geometric Measure Theory

Rectifiable sets, currents, and Federer's program.


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Geometric Measure Theory. Rectifiable sets, currents, and Federer’s program.

Foundations and canonical references

The standard treatments of geometric measure theory approach the subject from complementary angles. Federer, Geometric Measure Theory (1969) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Maggi, Sets of Finite Perimeter and Geometric Variational Problems (2012) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for geometric measure theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 1969
    Geometric Measure Theory
    federer-1969
  • textbook · primary · 2012
    Sets of Finite Perimeter and Geometric Variational Problems
    maggi-2012

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