Where H is the mean curvature of \ Sigma _ t and \ nu is the unit vector opposite of the mean curvature direction, then
22.
In differential geometry, "'constant-mean-curvature ( CMC ) surfaces "'are surfaces with constant mean curvature.
23.
The surface is trapped if both the null expansions ? ?are negative, signifying that the mean curvature vector is timelike and future directed.
24.
The sum of these quantities gives the mean curvature ( zero since the helicoid is a minimal surface ) and the product gives the Gaussian curvature.
25.
*PM : mean curvature at surface point, id = 9830 new !-- WP guess : mean curvature at surface point-- Status:
26.
*PM : mean curvature at surface point, id = 9830 new !-- WP guess : mean curvature at surface point-- Status:
27.
Specific examples of vector flows include the geodesic flow, the Hamiltonian flow, the Ricci flow, the mean curvature flow, and the Anosov flow.
28.
He has studied higher co-dimensional mean curvature flow extensively, leading to criteria relating to the flow's existence, regularity, and convergence.
29.
The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young-Laplace equation.
30.
This did not implement Mach's principle, because the predictions of general relativity in constant mean curvature gauge depend on the choice of clocks and rods.
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