Mathematical snapshots from the computational geometry landscape.
Matroid polytopes, nested sets and Bergman fans.
Maximum Density Space Packing with Parallel Strings of Spheres.
Mean Projections and Finite Packings of Convex Bodies.
Mehrfache gitterförmige Kreis- und Kugelanordnungen.
Methods of Perfect Coloring
Metric Entropy of Homogeneous Spaces
For a precompact subset K of a metric space and ε > 0, the covering number N(K,ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In this paper we give asymptotically correct estimates for covering numbers for a large class of homogeneous...
Minimality of toric arrangements
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.
Minimum Area of Circumscribed Polygons.
Minimum Dissection of a Rectilinear Polygon with Arbitrary Holes into Rectangles.
Minkowski's Successive Minima and the Zeros of a Convexity-Function.
Moments of inertia associated with the lozenge tilings of a hexagon.
Monomer-dimer tatami tilings of rectangular regions.
Motion of spirals by crystalline curvature
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Movable configurations.
Multigrid-convergence of digital curvature estimators
Many methods have been proposed to estimate differential geometric quantities like curvature(s) on discrete data. A common characteristics is that they require (at least) one user-given scale or window parameter, which smoothes data to take care of both the sampling rate and possible perturbations. Digital shapes are specific discrete approximation of Euclidean shapes, which come from their digitization at a given grid step. They are thus subsets of the digital plane . A digital geometric estimator...
Multiple Lattice Packings and Coverings of Spheres.
Multiple tilings by cubes with no shared faces.
Multiple Tilings of n-Dimensional Space by Unit Cubes.