22

Excess and the height bound

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

see Figure 22.1. The **spherical excess ...**

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