5 problems

For $p>p_c$, let $\widehat{W}_p$ denote the normalized Wulff crystal associated with the isoperimetric problem for supercritical bond percolation on $\mathbb{Z}^2$, and let…

Let $K(\theta)$ be the directional spreading speed and define the Wulff shape by … Let $\hat{\mathscr{F}}$ be the convex hull of the Frank diagram, let…

Fix a supercritical bond-percolation parameter $p$ and let $\mathcal{R}_p$ be the collection of continuum minimizers arising in the limiting isoperimetric problem. Let $W_p$ denote…

For bond percolation in two dimensions, let $p_c(2)$ be the critical percolation parameter and let the Wulff crystal denote the associated anisotropic isoperimetric minimizer for…

Let $S=S(\beta)\subset\mathbb{R}^2$ be a deterministic set whose translates approximate the normalized range of the walk in Hausdorff distance, and let $d_{\mathrm{Haus}}$ denote H…