25 research outputs found
The existence of thick triangulations -- an "elementary" proof
We provide an alternative, simpler proof of the existence of thick
triangulations for noncompact manifolds. Moreover, this proof
is simpler than the original one given in \cite{pe}, since it mainly uses tools
of elementary differential topology. The role played by curvatures in this
construction is also emphasized.Comment: 7 pages Short not
Intersecting all edges of convex polytopes by planes
AbstractA characterization theorem is given for 3-dimensional convex polytopes Q having the following property: There exists a polytope P, isomorphic to Q, all edges of which can be cut by a pair of planes that miss all its vertices. The result yields an affirmative solution of a conjecture of B. Grünbaum