We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact manifold without boundary the holonomies of properly convex structures form an open subset of the representation variety. We also give a relative version fo...

A liquid bridge between two balls will have a free surface which has constant mean curvature, and the angles of contact between the free surface and the fixed surfaces of the balls will be constant (although there might be two different contact angles: one for each ball). If we consider rotationally symmetric bridges, then the free surface must be a Delaunay surface, which may be classified as ...

The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in R3, two points s, t ∈ P , and a parameter ε > 0, it computes a path between s and t on P whose lengt...

Excitation of localized and delocalized surface plasmon resonances can be used for turning excellent reflectors of visible light, such as gold and silver, into efficient absorbers, whose wavelength, polarization or angular bandwidths are however necessarily limited owing to the resonant nature of surface plasmon excitations involved. Nonresonant absorption has so far been achieved by using comb...

Abstract We prove several estimates for the volume, mean width, and value of Wills functional sections convex bodies in John’s position, as well their polar bodies. These extend some well-known results position to case lower-dimensional sections, which had mainly been studied cube regular simplex. Some centrally symmetric minimal surface area are also obtained.

The influence of programming strain and temperature on the shape memory effect and surface morphology in programmed polycarbonate (PC) samples via uni-axial stretching is investigated. It is found that the samples programmed at around the glass transition start temperature not only have micro-cracks on their surface, but also show a necking phenomenon. Furthermore, the surface of the necked are...

In this paper we want to introduce an algorithm for the creation of polyhedral approximations for objects represented as strongly connected sets of voxels in three-dimensional binary images. The algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background ...

We show that a PL-realization of a closed connected manifold of dimension n − 1 in R (n ≥ 3) is the boundary of a convex polyhedron if and only if the interior of each (n− 3)-face has a point, which has a neighborhood lying on the boundary of a convex n-dimensional body. This result is derived from a generalization of Van Heijenoort’s theorem on locally convex manifolds to the spherical case. O...

We prove that for constant contact angle γ = 0, a capillary surface over a convex domain has no umbilical points unless that the surface is a hemisphere. The method involves the comparison of a lower hemisphere with the given surface at a second-ordered contact point and it is based on an argument of Alexandrov. © 2005 Elsevier B.V. All rights reserved.