# Mean curvature as an elliptic operator

Hi,

maybe this question will appear a little bit vague. How well is it known that the mean curvature on a hypersurface is a uniformly elliptic operator? For people from differential geometry this may be well-known, but I would like to see a proof of this. Can you please give me some references for good exposition on this matter?

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Hint: the first question you need to ask yourself is "What is the mean curvature operator acting on?" It outputs a number, but what is its input? –  Willie Wong Jul 11 '10 at 22:59