First variation of area formula
- First variation of area formula
In Riemannian geometry, the first variation of area formula relates the mean curvature of a hypersurface to the rate of change of its area as it evolves in the outward normal direction.
Let be a smooth family of oriented hypersurfaces in a Riemannian manifold "M" such that the velocity of each point is given by the outward unit normal at that point. The first variation of area formula is
:
where "dA" is the area form on induced by the metric of "M", and "H" is the mean curvature of .
References
*Chow, Lu, and Ni, "Hamilton's Ricci Flow." AMS Science Press, GSM volume 77, 2006.
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