Communications in Analysis and Geometry
Volume 18 (2010)
The maximum principle for minimal varieties of arbitrary codimension
Pages: 421 – 432
We prove that an $m$-dimensional minimal variety in a Riemannianmanifold cannot touch the boundary at a point where the sum of thesmallest $m$ principal curvatures is greater than 0. We prove astronger maximum principle in case the variety is a hypersurface.We also prove analogous results for varieties with bounded mean curvature.