Some isoperimetric inequalities in the plane with radial power weights

I McGillivray

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arXiv · 2104.01961

Some isoperimetric inequalities in the plane with radial power weights

I McGillivray

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Abstract

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 $α-β+1>0$, $α\leq 2β$ and $α(β+1)\leqβ^2$ except in the case $α=β=0$ which corresponds to the classical isoperimetric inequality.

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I McGillivray. 2021-04-05. Some isoperimetric inequalities in the plane with radial power weights. https://arxiv.org/abs/2104.01961

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