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‖...

Polyhedra of minimal surface area are suggested as natural candidates for object models. The problem of computing such a polyhedron from a set of 3D points that are its vertices is explored. An approximate algorithm is suggested, and results of a preliminary implementation are discussed.

This answers affirmatively a question posed in [CM04]. In [CM99], T. H. Colding and W. P. Minicozzi II proved an analogous theorem, stating that there exists an open set of metrics on M such that there are embedded minimal tori of arbitrarily large area. This result was extended to surfaces of positive genus in [Dea03] by B. Dean. The genus zero case has remained an open problem since then, lar...

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...

Surfaces formed by extracellular polymeric substances enclosing individual and some small communities of Acidithiobacillus ferrooxidans on plates of hydrophobic silicon and hydrophilic mica are analyzed by means of atomic force microscopy imaging. Accurate nanoscale descriptions of such coverage surfaces are obtained. The good agreement with the predictions of a rather simple but realistic theo...

For a bounded Lipschitz domain Ω, we show the existence of a measurable set D ⊂ ∂Ω of given area such that the first eigenvalue of the Laplacian with Dirichlet conditions on D and Neumann conditions on ∂Ω \D becomes minimal. If Ω is a ball, D will be a spherical cap.

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...

Gabor feature space is elaborated for representation, processing and segmentation of textured images. As a first step of preprocessing of images represented in this space, we introduce an algorithm for Gabor feature space denoising. It is a geometric-based algorithm that applies diffusion-like equation derived from a minimal weighted area functional, introduced previously and applied in the con...

The Plateau–Bézier problem consists in finding the Bézier surface with minimal area from among all Bézier surfaces with prescribed border. An approximation to the solution of the Plateau–Bézier problem is obtained by replacing the area functional with the Dirichlet functional. Some comparisons between Dirichlet extremals and Bézier surfaces obtained by the use of masks related with minimal surf...

Video-on-Demand (VoD) services require frequent updates in file configuration on the storage subsystem, so as to keep up with the frequent changes in movie popularity. This defines a natural reconfiguration problem in which the goal is to minimize the cost of moving from one file configuration to another. The cost is incurred by file replications performed throughout the transition. The problem...