Mathematics – Metric Geometry
Scientific paper
2006-07-06
Mathematics
Metric Geometry
13 pages, 3 figures
Scientific paper
We wish to draw attention to an interesting and promising interaction of two theories. On the one hand, it is the theory of \textbf{pseudo-triangulations} which was useful for implicit solution of thecarpenter's rule problem and proved later to give a nice tool for graph embeddings. On the other hand, it is the theory of hyperbolic virtual polytopes which arose from an old uniqueness conjecture for convex bodies (A. D. Alexandrov's problem): suppose that a constant $C$ separates (non-strictly) everywhere the principal curvature radii of a smooth 3-dimensional convex body $K$. Then $K$ is necessarily a ball of radius $C$. The two key ideas are: Passing from planar pseudo-triangulations to spherical pseudo-tilings, we avoid non-poited vertices. Instead, we use pseudo-di-gons. A theorem on spherically embedded Laman-plus-one graphs is announced. The difficult problem of hyperbolic polytopes constructing can be reduced to finding spherically embedded graphs.
No associations
LandOfFree
Planar pseudo-triangulations, spherical pseudo-tilings and hyperbolic virtual polytopes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Planar pseudo-triangulations, spherical pseudo-tilings and hyperbolic virtual polytopes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Planar pseudo-triangulations, spherical pseudo-tilings and hyperbolic virtual polytopes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-45580