Related papers: Visibility-preserving convexifications using singl…
Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects that bear a deformation content. By refining the resolution of the surface deformation gradient afforded by the polar decomposition theorem, we…
The classical Cauchy rigidity theorem for convex polytopes reads that if two convex polytopes have isometric developments then they are congruent. In other words, we can decide whether two polyhedra are isometric or not by using their…
We describe the space-time model of a uniformly rotating frame of reference satisfying the Helmholtz free mobility postulate, as we implemented it in a preceding article \cite{Bel1}, and we discuss the implications of this model as it…
We prove the existence of a finite set of moves sufficient to relate any two representations of the same 3-manifold as a 4-fold simple branched covering of S^3. We also prove a stabilization result: after adding a fifth trivial sheet two…
We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…
Various authors have investigated the problem of light deflection by radially moving gravitational lenses - with inconsistent results. In this paper we generalize the calculations for arbitrary lens velocities and show that, to first order…
This paper studies the configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there are no configurations in which all the edges lie along a line. The main results are that,…
A direct very simple proof that there can be no closed trapped surfaces (ergo no black hole regions) in spacetimes with all curvature scalar invariants vanishing is given. Explicit examples of the recently introduced ``dynamical horizons''…
An answer to the question: Can, in general, the adoption of a given symmetry induce a further symmetry, which might be hidden at a first level? has been attempted in the context of differential geometry of locally homogeneous spaces. Based…
We develop a deterministic large-time mechanism yielding Ces{\`a}ro asymptotic observability inequalities from moving localized observations for conservative evolutions. On each observation interval, exact convexification on a compact…
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and,…
We disprove a conjecture of A. Koldobsky asking whether it is enough to compare $(n-2)$-derivatives of the projection functions of two symmetric convex bodies in the Shephard problem in order to get a positive answer in all dimensions.
The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More generally, we can consider the problem of finding (if possible) two points in $A$ and $B$,…
A terrain T is an x-monotone polygonal chain in the plane; T is orthogonal if each edge of T is either horizontal or vertical. In this paper, we give an exact algorithm for the problem of guarding the convex vertices of an orthogonal…
We prove that the torsion of any closed space curve which bounds a simply connected locally convex surface vanishes at least 4 times. This answers a question of Rosenberg related to a problem of Yau on characterizing the boundary of…
In convex geometry, the constructions that assign to a convex body its difference body, projection body, or volume have the following properties: They are (1) invariant under volume-preserving linear changes of coordinates; (2) continuous;…
A dynamics of spatially extended particles, hidden in the dynamics of line solitons in more than one space dimension, is revealed through conservation laws obeyed by the single-soliton solution. These are functions of the solution of a…
The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a…
We conjecture that a convex polytope is uniquely determined up to isometry by its edge-graph, edge lengths and the collection of distances of its vertices to some arbitrary interior point, across all dimensions and all combinatorial types.…