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arxiv: 1610.05830 · v2 · pith:RGD2BGBUnew · submitted 2016-10-19 · 🧮 math.MG · math.DG

Balls Isoperimetric in mathbb{R}^n with Volume and Perimeter Densities r^m and r^k

Leonardo Di Giosia , Jahangir Habib , Lea Kenigsberg , Dylanger Pittman , Weitao Zhu This is my paper
classification 🧮 math.MG math.DG
keywords ballsdensitiesisoperimetricmathbbperimetervolumeassumptionconjecture
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We have discovered a "little" gap in our proof of the sharp conjecture that in $\mathbb{R}^n$ with volume and perimeter densities $r^m$ and $r^k$, balls about the origin are uniquely isoperimetric if $0 < m \leq k - k/(n+k-1)$, that is, if they are stable (and $m > 0$). The implicit unjustified assumption is that the generating curve is convex.

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