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Article overview
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Moebius rigidity for compact deformations of negatively curved manifolds | Kingshook Biswas
; | Date: |
12 Dec 2018 | Abstract: | Let $(X, g_0)$ be a complete, simply connected Riemannian manifold with
sectional curvatures $K_{g_0}$ satisfying $-b^2 leq K_{g_0} leq -1$ for some
$b geq 1$. Let $g_1$ be a Riemannian metric on $X$ such that $g_1 = g_0$
outside a compact in $X$, and with sectional curvatures $K_{g_1}$ satisfying
$K_{g_1} leq -1$. The identity map $id : (X, g_0) o (X, g_1)$ is
bi-Lipschitz, and hence induces a homeomorphism between the boundaries at
infinity of $(X, g_0)$ and $(X, g_1)$, which we denote by $hat{id}_{g_0, g_1}
: partial_{g_0} X o partial_{g_1} X$. We show that if the boundary map
$hat{id}_{g_0, g_1}$ is Moebius (i.e. preserves cross-ratios), then it extends
to an isometry $F : (X, g_0) o (X, g_1)$. | Source: | arXiv, 1812.4888 | Services: | Forum | Review | PDF | Favorites |
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