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Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory by Francesco Maggi

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25

Harmonic approximation and excess improvement

Let us now briefly sketch a picture of the situation after the results proved in the previous chapters. For the sake of clarity, in this overview, we shall directly refer to the case of a perimeter minimizer E in an open cylinder C(x0, r0), with xo images images (thus, images = 0). In the Lipschitz approximation theorem, Theorem 23.7, we have shown the existence of two constants and such that if e(E, x0, 9 r, ) ≤ ...

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