Take the 2-minute tour ×  Gromov-Hausdorff distance between two
compact manifolds measures how far away the manifolds are from
being isometric. (Wikipedia: http://en.wikipedia.org/wiki/Gromov
%E2%80%93Hausdorff_convergence) In many cases it is possible to
do coarse estimates and conclude that a sequence of manifolds
converges or diverges.  How does one usually go about
calculating GH distance precisely?  Example: Take two spheres of
different radii $r$ and $R$ with intrinsic (i.e the distance
between two points is the length of the arc of a great circle
that connects them) metrics obtained from standard embeddings
into $\Bbb R^n$. What is the GH distance between them?
share|improve this question I once asked Dima Burago this
question, and his response was that (a) there are very few pairs
of spaces for which the precise GH distance is known and (b) he
could not think of a single reason off the top of his head why
one would want to know. As you say, it is mainly useful to know
when it is finite and when a sequ