# Lower bound on volume of minimal hypersurface contained in a unit ball with curvature bounds

I was just wondering, if I have a geodesic ball of radius one in a manifold M whose sectional curvature lies between -epsilon and epsilon for epsilon small, and the injectivity radius of my manifold is two say, and I have a SINGULAR minimal hypersurface in M passing through the centre of my unit ball, can I find a lower bound, away from zero, on the volume of the singular minimal hypersurface contained in the ball, in terms of only the dimension of the ambient manifold M? Thanks!

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I know nothing about this stuff. Is such a bound already known if M is flat? –  Deane Yang Oct 26 '09 at 14:10