Mathematics – Differential Geometry
Scientific paper
2007-04-17
Mathematics
Differential Geometry
14 pages
Scientific paper
In this paper we consider three-manifolds with weakly umbilic boundary (the Second Fundamental form of the boundary is a constant multiple of the metric). We show that if the initial manifold has positive Ricci curvature and the boundary is convex (nonnegative Second Fundamental form), its metric can be deformed via the Ricci flow to a metric of constant curvature and totally geodesic boundary.
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