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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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22

Excess and the height bound

We now introduce the notion of excess, a key concept in the regularity theory for (Λ, r0)-perimeter minimizers. Given a set of locally finite perimeter E in images, the cylindrical excess of E at the point x images imagesE, at the scale r > 0, and with respect to the direction v images Sn–1, is defined as

see Figure 22.1. The spherical excess ...

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