Federer | Geometric Measure Theory Pdf !exclusive!

This 700+ page book is the foundational text of geometric measure theory (GMT). It remains the definitive reference for the field’s core results: area/coarea formulas, rectifiability, current theory, and the Plateau problem.

Geometric measure theory was born out of a desire to solve a centuries-old problem. The , named after the 19th-century physicist Joseph Plateau, asks for the existence of a surface of minimal area spanning a given closed boundary curve. While the problem had been tackled as early as 1760 by Lagrange, and partially solved in the 1930s by Jesse Douglas and Tibor Radó, their solutions came with significant topological restrictions. federer geometric measure theory pdf