**Analysis of the Jante’s Law Process and Proof of Conjecture: Abstract and Introduction**

by Keynesian TechnologySeptember 11th, 2024

**Authors:**

(1) Edward Crane, School of Mathematics, University of Bristol, BS8 1TH, UK;

(2) Stanislav Volkov, Centre for Mathematical Sciences, Lund University, Box 118 SE-22100, Lund, Sweden.

Reduction to the case of uniform geometry

All original points are eventually removed, a. s.

Acknowledgements and References

In this section, we complete the proof of Theorem 2. By Lemma 10 it suffices to prove the absolute continuity of the limit point ξ for a B-valued Jante’s law process where B is bounded. So we shall assume throughout this section that B is bounded, and therefore has uniform geometry.

We will need an isoperimetric inequality for inner shells of convex bodies, for which we have been unable to find a reference. It concerns the following problem. Suppose you have a (possibly) hollow chocolate egg whose outer boundary is the boundary of a convex body. If all the chocolate is within distance r of the outer boundary of the egg, what is the maximum quantity of chocolate that can possibly be contained within a ball of radius R? See Figure 4.

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8 Think of δ small and ∆ large.

L O A D I N G

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