Einige Bemerkungen über die Existenz orientierter Mannigfaltigkeiten mit vorgeschriebener mittlerer Krümmungsform

Abstract

Given an integral $m$-current $T_o$ in $\mathbb R^{m+k}$ and a tensor $H$ of type $(m,1)$ on $\mathbb R^{m+k}$ with values orthogonal to each of its arguments we prove under suitable smallness conditions the existence of an integral $m$-current $T$ with boundary $\partial T = \partial T_o$ aI having prescribed mean curvature form $H$.