The global geometry of surfaces with prescribed mean curvature in\n $\\mathbb{R}^3$

We develop a global theory for complete hypersurfaces in $\\mathbb{R}^{n+1}$\nwhose mean curvature is given as a prescribed function of its Gauss map. This\ntheory extends the usual one of constant mean curvature hypersurfaces in\n$\\mathbb{R}^{n+1}$, and also that of self-translating solitons of the mean\ncurvature flow. For the particular case $n=2$, we will obtain results regarding\na priori height and curvature estimates, non-existence of complete stable\nsurfaces, and classification of properly embedded surfaces with at most one\nend.\n