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8.5.4.2 Mean curvature

Color Plate A.4 shows a color map of the mean curvature $ H $ . Because of anti-symmetry with respect to $ u = 0.5$ , mean curvature has $ H=0$ contour line at $ u = 0.5$ . Mean curvature varies from $ -4.056$ to $ 4.056$ . Both global maximum and minimum curvature are located inside the domain at $ (0.190, 0.414)$ and $ (0.810, 0.414)$ respectively. There are seven local maxima and seven local minima along the boundary. The local maxima are located at $ (0.116, 0)$ , $ (0.319, 0)$ , $ (0.789, 0)$ , $ (0.211, 1)$ , $ (0,0.089)$ , $ (0,0.861)$ , $ (1, 0.440)$ with $ H\;=\;0.539$ , $ 0.539$ , $ -0.524$ , $ 0.121$ , $ 1.155$ , $ 1.155$ , $ -0.607$ . The local minima are located at $ (0.211, 0)$ , $ (0.681, 0)$ , $ (0.884,0)$ , $ (0.789, 1)$ , $ (0, 0.440)$ , $ (1,0.089)$ , $ (1,0.861)$ with $ H\;=\;0.524$ , $ -0.539$ , $ -0.539$ , $ -0.121$ , $ 0.607$ , $ -1.155$ , $ -1.155$ . Since the local maximum and minimum inside the domain are on the same iso-parametric line $ v=0.414$ , we subdivide into two sub-domains at this line.

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Next: 8.5.4.3 Maximum principal curvature Up: 8.5.4 Examples Previous: 8.5.4.1 Gaussian curvature   Contents   Index
December 2009