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 In this talk we wiill work towards proving the following theorem: a contractible 3-manifold with positive scalar curvature and bounded geometry must be diffeomorphic to R^3. The proof involves running an innermos In this talk we will work towards proving the following theorem: a contractible 3-manifold with positive scalar curvature and bounded geometry must be diffeomorphic to R^3. The proof involves running an innermost In this talk we will work towards proving the following theorem: a contractible 3-manifold with positive scalar curvature and bounded geometry must be diffeomorphic to R^3. The proof involves running an innermost weak inverse mean curvature flow on the manifold. This talk is based on joint work with Otis Chodosh and Yi Lai. weak inverse mean curvature flow on the manifold. This talk is based on joint work with Otis Chodosh and Yi Lai.t weak inverse mean curvature flow on the manifold. This talk is based on joint work with Otis Chodosh and Yi Lai.

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