We propose causal fermion systems and Riemannian fermion systems as a framework for describing spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples like the Euclidean plane, the two-dimensional Minkowski space, a conical...

A 3D surface classification method based upon the quadric surface model is described. This technique does not require the points from the surface to lie on a grid. A sample of surface points is classified as planar or nonplanar through two hypothesis testa If the sample is nonplanar, curvature features are evaluated at each point to classify the sample as spherical, cylindrical, or conical. A n...

Geometric problems originating in architecture can lead to interesting research and results in geometry processing, computer aided geometric design, and discrete differential geometry. In this article we survey this development and consider an important problem of this kind: Discrete surfaces (meshes) which admit a multi-layered geometric support structure. It turns out that such meshes can be ...

Singularities of the mean curvature flow an embedded surface in R^3 are expected to be modelled on self-shrinkers that compact, cylindrical, or asymptotically conical. In order understand before and after singular time, it is crucial know uniqueness tangent flows at singularity. all dimensions, assuming singularity multiplicity one, compact case has been established by second-named author, cyli...

A special arrangement of spinning strings with dislocations similar to a von Kármán vortex street is studied. We numerically solve the geodesic equations for the special case of a test particle moving along two infinite rows of pure dislocations and also discuss the case of pure spinning defects. PACS numbers: 04.20 Jb, 04.50.+h, 11.10.Lm, 47.32.Cc Conical singularities or spacetime defects are...

It is known that the retrovirus capsids possess a fullerene-like structure. These caged polyhedral arrangements are built entirely fromhexagons and exactly 12 pentagons according to the Euler theorem. Viral capsids are composed of capsid proteins, which create the hexagon and pentagon shapes by groups of six (hexamer) and five (pentamer) proteins. Different distributions of these 12 pentamers r...