We consider the punctured plane with volume density ∣x∣α and perimeter density ∣x∣β. We show that centred balls are uniquely isoperimetric for indices (α,β) which satisfy the conditions α−β+1>0, α≤2β and α(β+1)≤β2 except in the case α=β=0 which corresponds to the classical isoperimetric inequality.
@article{arxiv.2104.01961,
title = {Some isoperimetric inequalities in the plane with radial power weights},
author = {I McGillivray},
journal= {arXiv preprint arXiv:2104.01961},
year = {2021}
}