321 research outputs found
Similarity and symmetry measures for convex sets based on Minkowski addition
This paper discusses similarity and symmetry measures for convex shapes. Their definition is based on Minkowski addition and the Brunn-Minkowski inequality. All measures considered are invariant under translations; furthermore, they may also be invariant under rotations, multiplications, reflections, or the class of all affine transformations. The examples discussed in this paper allow efficient algorithms if one restricts oneselves to convex polygons. Although it deals exclusively with the 2-dimensional case, many of the theoretical results carry over almost directly to higher-dimensional spaces. Some results obtained in this paper are illustrated by experimental data
Some open questions on anti-de Sitter geometry
We present a list of open questions on various aspects of AdS geometry, that
is, the geometry of Lorentz spaces of constant curvature -1. When possible we
point out relations with homogeneous spaces and discrete subgroups of Lie
groups, to Teichm\"uller theory, as well as analogs in hyperbolic geometry.Comment: Not a research article in the usual sense but rather a list of open
questions. 19 page
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