I. McGillivray

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20112021

most citedAn isoperimetric inequality in the plane with a log-convex density

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math.DG2021

Some isoperimetric inequalities in the plane with radial power weights

I McGillivray

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 t…

math.DG2016★ 1 cited

An isoperimetric inequality in the plane with a log-convex density

I. McGillivray

Given a positive lower semi-continuous density $f$ on $R^{2}$ the weighted volume $V_{f} := f L^{2}$ is defined on the $L^{2}$ -measurable sets in $R^{2}$ .…