Infinite distance components of the boundary of moduli spaces of conformal structures (Q1304658)

The author continues his investigation (started in a previous joint paper with J.~Jost) of the \(L^2\)-geometry of moduli spaces \(B^+\) of conformal structures, where the \(L^2\)-metric is induced from the canonical metrics for conformal structures that supports a positive scalar curvature metric. He considers the \(L^2\)-metric on \(B^+\) as well as on the moduli space \(B^+_0\) of locally conformally flat structures in the direction of decreasing Yamabe invariant. It is proved that in dimension 3 and 4 a boundary point of \(B^+\) and \(B^+_0\) respectively which can be represented by a Riemannian metric with vanishing scalar curvature has infinite distance from inner points. The calculations presented indicate that in dimension bigger than 4 the distance of a boundary point of \(B^+_0\) as above from the interior is finite.