Moduli Space Theory of Constant Mean Curvature Hypersurfaces

In this paper, we study the set of complete noncompact hypersurfaces in R(n+1) which have constant mean curvature equal to 1. and a finite number of ends. By means of the application of the, implicit function theorem, we will prove that this set has a smooth structure near any nondegenerale element,. We start by a review of the functional properties of elliptic operators acting on functions defined oil a manifold with cylindrical ends. This will explain the central role played by the indicial roots about an n-Delaunay hypersurface. Then, we will explain how to apply the implicit function theorem in our setting. We partially generalize, in any dimension, the results of R.. Kusner, R. Mazzeo and D. Pollack.