We will present joint work with Gerhard Huisken on a fully nonlinear flow for hypersurfaces in Riemannian manifolds. Unlike mean curvature flow, this flow preserves two-convexity in a general ambient manifold. For this fully nonlinear flow, we establish a convexity estimate, a cylindrical estimate, and a pointwise curvature derivative estimate. These estimates allow us to extend the flow beyond singularities by a surgery procedure, similar to the ones developed by Hamilton and Perelman for the Ricci flow and by Huisken and Sinestrari for mean curvature flow

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