Stability and curvature estimates for minimal graphs with flat normal bundles

Details Stability and curvature estimates for minimal graphs with flat normal bundles Stability and curvature estimates for minimal graphs with flat normal bundles

2004-11-08

arxiv.org/abs/math/0411169v2

Mathematics

Differential Geometry

Theorem 1.2 is mistakenly stated. It is replaced by the statement of Corollary 1.1

Scientific paper

It is well-known that a minimal graph of codimension one is stable, i.e. the second variation of the area functional is non-negative. This is no longer true for higher codimensional minimal graphs. In this note, we prove that a minimal graph of any codimension is stable if its normal bundle is flat. We also prove minimal graphs of dimension no greater than six and any codimension is flat if the the normal bundle is flat and the density at infinity is finite. Such a Bernstein type theorem holds in any dimension if we assume additionally growth conditions on the volume element.

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