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Tangent cones to two-dimensional area-minimizing integral currents are unique. (English) Zbl 0538.49030
The author proves uniqueness of tangent cones for two dimensional integral currents in \(R^ n\). He reduces the problem to an ”epiperimetric” inequality which is proved by constructing a comparison surface from the graph of a multiple-valued harmonic function, whose area he estimates in terms of the Fourier series of its boundary values.
Reviewer: R.Schianchi

MSC:
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
28A75 Length, area, volume, other geometric measure theory
58A25 Currents in global analysis
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
53C65 Integral geometry
58C35 Integration on manifolds; measures on manifolds
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