Calculus of variations and optimal control; optimization Geometric measure theory and optimization on manifolds Concept
Integral current
Summary
An integral current is a current that behaves like an oriented surface with integer multiplicities. It is given by integration over a rectifiable set with an orientation and a positive integer multiplicity. Both it and its boundary have finite mass. Integral currents include all compact oriented smooth submanifolds with boundary. By the Federer–Fleming compactness theorem, they are closed under the limits that matter for area minimisation. They are the setting of the Plateau problem in all dimensions and codimensions.
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| Tag | EG4AJVEFT2 |
|---|---|
| URI | m2://EG4AJVEFT2 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 49Q15, 28A75 |
| Specializes | Current |
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