Syllabus
1. Rectifiable sets Rectifiability Tangent spaces C-1 approximation Densities Differential forms and currents
2. BV functions of several variables Essential variations on lines Convergence of BV functions (strong, weak, strict) Pointwise properties of BV functions
3. Sets of finite perimeter Federer boundary and its rectifiability Gauss-Green theorem Characterization by the essential boundary
4. Lipschitz manifolds Lipschitz atlas Orientation Stokes theorem
Annotation
Sets of finite perimeter, Gauss-Green theorem, pointwise properties of BV functions, Stokes theorem for nonsmooth data, rectifiability, definition of currents. Recommended for master students of mathematical analysis.