Maximum principle at infinity for complete minimal surfaces in flat 3-manifols
The author studies the maximum principle at infinity for minimal surfaces with noncompact boundaries. The main result is as follows: Let \(M_1\) and \(M_2\) be disjoint, properly embedded, stable minimal surfaces with noncompact boundaries in a complete flat 3-manifold. Then \(\text{dist}(M_1,M_2)=\min(\text{dist}(\partial M_1,M_2),\text{dist}(M_1,\partial M_2))\). If the boundary of one surface, say \(M_1\), is empty, then \(\text{dist}(M_1,M_2)= \text{dist}(M_1,\partial M_2)\).
scientific article; zbMATH DE number 780909
scientific article