We expect that all compact Ricci flat manifolds (with the metric defined up to a constant scalar factor) appear as target spaces of degenerating CFTs. Thus, the construction of the compactification of the moduli space of CFTs should include as a part a compactification of the moduli spaces of Einstein manifolds. Notice that in differential geometry there is a fundamental result of Gromov (see [G]) about the precompactness of the moduli space of pointed connected complete Riemannian manifolds of a given dimension, with the Ricci curvature bounded from below. One can speculate about the relationship between the compactification of the moduli space of CFTs and the Gromov’s compactification. For example, is it true that all target spaces appearing as limits of CFTs have non-negative Ricci curvature?