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I am reading the Colding and Minicozzi book "A course in Minimal Surfaces".
I have a question regarding one of the points mentioned in the book. I want to prove that a minimal hypersurface which is a graph in $\mathbb{R}^n$ is area minimizing.

My idea is - if $\omega$ is the volume form in $\mathbb{R}^n$ and $N$ is the normal vector then ${\iota_N\omega}$ must be a calibration and hence the hypersurface will be a calibrated submanifold and hence area minimizing.

Is it correct ?

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    Are you trying to prove the stability or that they are actually area minimizing? – 2017-02-23
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    I need only stability though but I think we can easily see that if we can prove that it is area minimizing. – 2017-02-23

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