I. McGillivray

activity

20112021

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

1 citations · 1 across the 4 of their papers we have counts for

collaborators

5 papers

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.AP2017

A weighted isoperimetric inequality on the hyperbolic plane

I. McGillivray

We prove a counterpart of the log-convex density conjecture in the hyperbolic plane.

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 $R^{2}$ .…

math.AP2011

Riesz-type inequalities and maximum flux exchange flow

I E McGillivray

Let $D$ stand for the open unit disc in $R^{d}$ ( $d \geq 1$ ) and $(D, B, m)$ for the usual Lebesgue measure space on $D$ . Let $H$ stand for the real Hil…

math.SP2011

The spectral shift function for planar obstacle scattering at low energy

I E McGillivray

Let $H$ signify the free non-negative Laplacian on $R^{2}$ and $H_{Y}$ the non-negative Dirichlet Laplacian on the complement $Y$ of a nonpolar compact subset $K$ in the plane…