Related papers: Intersection properties of finite disk collections
We study the way in which the Euclidean subspaces of a Banach space fit together, somewhat in the spirit of the Ka\v{s}in decomposition. The main tool that we introduce is an estimate regarding the convex hull of a convex body in John's…
Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes.…
We consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p in R and q in B, we consider the disk through p and q with the smallest diameter. We prove that for any R and B…
We construct examples of compact and one-ended constant mean curvature surfaces with large mean curvature in Riemannian manifolds with axial symmetry by gluing together small spheres positioned end-to-end along a geodesic. Such surfaces…
The \v{C}ech complex is one of the most widely used tools in applied algebraic topology. Unfortunately, due to the inclusive nature of the \v{C}ech filtration, the number of simplices grows exponentially in the number of input points. A…
Observational manifestations of disturbances in a protoplanetary disk caused by a collision with a massive planet are studied. It is assumed that the planet moves along a parabolic trajectory that intersects the disk plane near the star.…
It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…
We study the set of intersection sizes of a k-dimensional affine subspace and a point set of size m \in [0, 2^n] of the n-dimensional binary affine space AG(n,2). Following the theme of Erd\H{o}s, F\"uredi, Rothschild and T. S\'os, we…
We study the intrinsic structure of parametric minimal discs in metric spaces admitting a quadratic isoperimetric inequality. We associate to each minimal disc a compact, geodesic metric space whose geometric, topological, and analytic…
In this work, the effects of excluded volume are studied in the "one to five hard disks in a box" system. For one and two disks in different types of cages, the attractive and repulsive forces are calculated analytically. Attractive forces…
We introduce an original notion of extra-fine sheaf on a topological space, and a variant (hyper-extra-fine) for which \v{C}ech cohomology in strictly positive degree vanishes. We provide a characterization of such sheaves when the…
We study the boundary of Teichmueller disks in a partial compactification of Teichmueller space, and their image in Schottky space. We give a broad introduction to Teichmueller disks and explain the relation between Teichmueller curves and…
We analyse properties of contact networks formed in packings of soft frictionless disks near the unjamming transition. We construct polygonal tilings and triangulations of the contact network that partitions space into convex regions which…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact…
We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs.
Motivated by the recent achievement of space-based Bose-Einstein condensates (BEC) with ultracold alkali-metal atoms under microgravity and by the proposal of bubble traps which confine atoms on a thin shell, we investigate the BEC…
Continuing the investigations of Harborth (1974) and the author (2002) we study the following two rather basic problems on sphere packings. Recall that the contact graph of an arbitrary finite packing of unit balls (i.e., of an arbitrary…
A triangulated piecewise-linear minimal surface in Euclidean 3-space defined using a variational characterization is critical for area amongst all continuous piecewise-linear variations with compact support that preserve the simplicial…
We study closed geodesics on hyperbolic surfaces, and give bounds for their angles of intersection and self-intersection, and for the sides of the polygons that they form, depending only on the lengths of the geodesics