Stability of hyperbolic manifolds with cusps under Ricci flow

Details Stability of hyperbolic manifolds with cusps under Ricci flow Stability of hyperbolic manifolds with cusps under Ricci flow

2010-04-12

arxiv.org/abs/1004.2058v2

Mathematics

Differential Geometry

48 pages, 4 figures; minor revisions, improved exposition

Scientific paper

We show that every finite volume hyperbolic manifold of dimension greater or equal to 3 is stable under rescaled Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Note that we do not need to make any decay assumptions on this perturbation. It will turn out that the main difficulty in the proof comes from a weak stability of the cusps which has to do with infinitesimal cusp deformations. We will overcome this weak stability by using a new analytical method developed by Koch and Lamm.

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