🚀 go-pugleaf

I believe that the following statement is true, but I have
been unable to find it in the literature
(by the way, I know that \beta(3,3,3,0) is false).



Assume that D_1,...,D_n (for n >= 2) are locally flat 3-cells
in Euclidian 3-space R^3 such that
all the D_i's have exactly one point p in common; i.e.,

	D_i \cap D_j = Bd D_i \cap Bd D_j = {p}
		for all pairwise distinct i and j.

If for each \epsilon > 0 there exists a flat 2-sphere R (e.g.
R is homeomorphic to S^2 and flat) such that

	p is contained in the interior of R,
	the diameter of R is smaller than \epsilon, and
	the sphere R intersects each D_i in a simple closed curve;
	
then the cells D_1,...,D_n are simultaneously flat; e.g., there
exists a "flattening" homeomorphism h of R^3 such that h(D_i) is a
simplex with h(p) as a vertex (for i=1,...,n).




Any suggestions, hints are welcome.

Thanks in advance.

(Le, Computer Science Dep.)

le@fuhainf.fernuni-hagen.de