Calculus of variations and optimal control; optimization Geometric measure theory and optimization on manifolds Concept
Flat norm
Summary
The flat norm measures the distance between two currents by the least total size of a decomposition. The difference is split into a small piece plus the boundary of a small filling. Two surfaces are close in the flat norm when they differ by a small area or bound a thin region. This holds even if their masses differ. Convergence in the flat norm is the natural convergence of generalised surfaces, and the Federer–Fleming compactness theorem is stated with it. It also gives the distance used in the comparison and approximation of integral currents.
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| Tag | Y7P66D41Z8 |
|---|---|
| URI | m2://Y7P66D41Z8 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 49Q15, 28A75 |
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