We study the heat kernel and the Green’s function on the infinite supercritical percolation cluster in dimension d ≥ 2 and prove a quantitative homogenization theorem for these functions with an ...
A set E on the real line of Hausdorff dimension 1 is constructed, such that the graph of E on the boundary of any C2 domain $\{t > \tau(x) \}$, or on the boundary of any $\operatorname{Lip} \frac{1}{2 ...
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