Maximum principles for submanifolds of arbitrary codimension and bounded mean curvature

Dierkes, Ulrich; Schwab, Dirk
February 2005
Calculus of Variations & Partial Differential Equations;Feb2005, Vol. 22 Issue 2, p173
Academic Journal
We construct quadratic forms onwhich are subharmonic on anyn-dimensional minimal submanifold inand, more generally, on submanifolds of bounded mean curvature. This leads to nonexistence results for connectedn-dimensional minimal submanifolds inas well as to necessary conditions for the existence of connected submanifolds of bounded mean curvature with arbitrary codimension. Furthermore we discuss a barrier principle forn-dimensional submanifolds inof bounded mean curvature.


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