| Positively curved compact Riemannian manifolds with boundary are studied from the viewpoint of extending the metric to a complete metric with positive Ricci curvature. Sufficient conditions on the boundary are given for manifolds bounded by a closed hypersurface in a sphere and other simple spaces.;Also, a large new class of compact manifolds with positive Ricci curvature is constructed, in a manner pertinent to the above extension problem. |
