منابع مشابه
Symmetric Convex Sets with Minimal Gaussian Surface Area
Abstract. Let Ω ⊆ R have minimal Gaussian surface area among all sets satisfying Ω = −Ω with fixed Gaussian volume. Let A = Ax be the second fundamental form of ∂Ω at x, i.e. A is the matrix of first order partial derivatives of the unit normal vector at x ∈ ∂Ω. For any x = (x1, . . . , xn+1) ∈ R, let γn(x) = (2π)−n/2e 2 1+···+x 2 n+1. Let ‖A‖2 be the sum of the squares of the entries of A, and...
متن کاملSymmetric Convex Sets with Minimal Gaussian Surface Area
Let Ω ⊆ R have minimal Gaussian surface area among all sets satisfying Ω = −Ω with fixed Gaussian volume. Let A = Ax be the second fundamental form of ∂Ω at x, i.e. A is the matrix of first order partial derivatives of the unit normal vector at x ∈ ∂Ω. For any x = (x1, . . . , xn+1) ∈ R, let γn(x) = (2π)−n/2e−(x 2 1+···+x 2 n+1. Let ‖A‖ be the sum of the squares of the entries of A, and let ‖A‖...
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We present a method for constructing tensor product Bezier surfaces from contour (cross-section) data. Minimal area triangulations are used to guide the surface construction, and the final surface reflects the optimality of the triangulation. The resulting surface differs from the initial triangulation in two important ways: it is smooth (as opposed to the piecewise planar triangulation), and i...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2014
ISSN: 0196-8858
DOI: 10.1016/j.aam.2014.08.006