Mathematics – Differential Geometry
Scientific paper
2012-02-04
Mathematics
Differential Geometry
52 pages, 9 figures
Scientific paper
We consider sequences of metrics, $g_j$, on a Riemannian manifold, $M$, which converge smoothly on compact sets away from a singular set $S\subset M$, to a metric, $g_\infty$, on $M\setminus S$. We prove theorems which describe when $M_j=(M, g_j)$ converge in the Gromov-Hausdorff sense to the metric completion, $(M_\infty,d_\infty)$, of $(M\setminus S, g_\infty)$. To obtain these theorems, we study the intrinsic flat limits of the sequences. A new method, we call hemispherical embedding, is applied to obtain explicit estimates on the Gromov-Hausdorff and Intrinsic Flat distances between Riemannian manifolds with diffeomorphic subdomains.
Lakzian Sajjad
Sormani Christina
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