What about minimal pairs of compact convex sets
that are equivalent to a pair of polytops?





We already know

Let X=R 2 and (A,B) be a minimal pair of compact convex sets in R 2. If (A,B) is equivalent to a pair of convex polygons then A and B are polygons.
Do you have a question?
Write to rich@amu.edu.pl ,
lh09@rz.uni-karlsruhe.de




We still do not know

Let (A,B) be a minimal pair of compact convex sets in R n, n > 2. Let (A,B) be equivalent to a pair of convex polytops. Do A and B have to be polytops?
Do you have an answer?
Write to rich@amu.edu.pl,
lh09@rz.uni-karlsruhe.de


* Do minimal pairs of convex sets exist? * Are minimal pairs of compact sets unique? *
* What about convex polytops? * What are invariants of minimal pairs of convex sets? *
* How do minimal pairs of convex sets relate to fractions? *
* History of minimal pairs of convex sets *
* How did we get interested in pairs of convex sets? *
* References * Definitions *
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