Bessa Pacelli, Universidade Federale de Ceara, Fortaleza, Stochastic half-space theorems for minimal surfaces and H-surfaces of $\mathbb{R}^{3}$.
ZoomIn the 1980s Xavier proved that a complete non-planar minimal surface with bounded curvature of $\mathbb{R}^{3}$ can not lie in half-space. In 1990, Hoffman-Meeks proved that this half-space property holds for properly immersed non-planar minimal surfaces of $\mathbb{R}^{3}$ as well. And they went further, proving what is called "the strong half-space theorem" that states that…