For any d â‰¥ 5 and k â‰¥ 3 we construct a family of Cayley graphs of degree d, diameter k, and order at least k((dâˆ’3)/3)k. By comparison with other available results in this area we show that, for allâ€¦ (More)

It is well known that pseudo Riemannian metrics in the projective class of a given torsion free a ne connection can be obtained from (and are equivalent to) the solutions of a certain overdeterminedâ€¦ (More)

We discuss the space of Einstein metrics, up to diffeomorphism, on a compact manifold. In particular we mention some heuristics on its dimension and some theorems on its compactness.

We prove versions of various standard inequalities in which the dependence of the constant on the metric is explicit. 1 Technical results Definition. Let (M, g) be a smooth Riemannian n-manifold andâ€¦ (More)