Density exp(±r^a)
An interesting class of densities for the isoperimetric problem on Rn is exp(±ra). The Log-convex Density Conjecture says that spheres about the origin are isoperimetric if and only if 0≤a≤1 with the minus sign or a ≥ 1 with the plus sign, known for a=2 [Borell; see Rosales et al.] and in R2 for a≥2 [Maurmann-Morgan]. Henceforth we’ll focus on R2. Continue reading ‘Density exp(±r^a)’ »
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