Almgren's minimal surfaces

Almgren's minimal surfaces are a mathematical concept describing surfaces that locally minimize their area, similar to a soap film stretching across a wireframe. Unlike smooth surfaces, these can be more complex and may include singularities or branching points. Almgren developed a rigorous framework to analyze these surfaces within geometric measure theory, allowing mathematicians to understand their structure, regularity, and behavior even in cases where traditional smooth descriptions fail. Essentially, his work extends our understanding of minimal surfaces to more general and intricate configurations, providing foundational tools for advanced geometric analysis.