We study the manifold of all metrics with the fixed volume form on a compact Riemannian manifold of dimension ≥ 3. We compute the characteristic function for the L (Ebin) distance to the reference metric. In the Appendix, we study Lipschitz-type distance between Riemannian metrics, and give applications to the diameter and eigenvalue functionals.

Recent developments in formulations for generating swept volumes have made a significant impact on the efficiency of employing such algorithms and on the extent to which formulations can be used in representing complex shapes. In this paper, we outline a method for employing the representation of implicit surfaces using the Jacobian rank deficiency condition presented earlier for the sweep of p...