Constraint maps and free boundaries
Alessio Figalli, Andr\'e Guerra, Sunghan Kim, and Henrik Shahgholian
TL;DR
This paper provides an overview of free boundary theory, emphasizing the vectorial case called constraint maps, including historical context and recent heuristic insights.
Contribution
It offers a concise exposition of classic and recent ideas in free boundary theory, focusing on the vectorial constraint maps and highlighting new heuristic results.
Findings
Historical perspective on free boundary problems
Recent heuristic-level results in constraint maps
Focus on vectorial free boundary theory
Abstract
In this short expository note, we present a selection of classic and recent ideas in free boundary theory, with a focus on the vectorial case, referred to here as constraint maps. The note includes a brief historical perspective and highlights the latest heuristic-level results.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Logic, programming, and type systems · Geometric and Algebraic Topology