For 0 ≤ α < β+1 and β ≤ 2α, the weighted perimeter ∫ y^α ds is minimized among sets of fixed weighted measure ∬ y^β dx dy in R²₊ by an explicit y-axis symmetric set.
Balls Isoperimetric in $\mathbb{R}^n$ with Volume and Perimeter Densities $r^m$ and $r^k$
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Some isoperimetric inequalities with respect to monomial weights
For 0 ≤ α < β+1 and β ≤ 2α, the weighted perimeter ∫ y^α ds is minimized among sets of fixed weighted measure ∬ y^β dx dy in R²₊ by an explicit y-axis symmetric set.