After appropriate normalizations an embedded disk whose second fundamental form has large norm contains a multi-valued graph, provided the L^P norm of the mean curvature is sufficiently small. This generalizes to non-minimal surfaces a well known result of Colding and Minicozzi.
Some geometric properties of hypersurfaces with constant $r$-mean curvature in Euclidean space
Nonlinear evolution by mean curvature and isoperimetric inequalities
Complex-valued extension of mean curvature for surfaces in Riemann-Cartan geometry
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