TL;DR
This survey reviews the fundamental concepts and roles of rectifiable sets, measures, currents, and varifolds across various mathematical fields including analysis, potential theory, and PDEs.
Contribution
It provides a comprehensive overview of rectifiability and its applications, synthesizing existing knowledge across multiple mathematical disciplines.
Findings
Summarizes key properties of rectifiable sets and measures.
Highlights the significance of rectifiability in complex and harmonic analysis.
Connects rectifiability to various mathematical theories and problems.
Abstract
This is a survey on rectifiability. I discuss basic properties of rectifiable sets, measures, currents and varifolds and their role in complex and harmonic analysis, potential theory, calculus of variations, PDEs and some other topics.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows