Abstract:In this note we investigate a problem formulated by Pleijel in 1955. It asks for the cone over a convex plane domain K having minimal surface among all cones over K with the same given height h. For cones based on reflection symmetric polygonal K we analyze the behaviour, as h → 0 and as h → ∞, of the position of the apex for the minimizing cone and characterize the coordinate of the limit points by necessary conditions. Furthermore, the question whether there are convex domains such that the minimal cone does… Show more
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