We model the dynamic geometry of a time-varying scene as a 3D isosurface in space-time. The intersection of the isosurface with planes of constant time yields the geometry at a single time instant. An optimal fit of our model to multiple video sequences is defined as the minimum of an energy functional. This functional is given by an integral over the entire hypersurface, which is designed to optimize photo-consistency. A PDE-based evolution derived from the Euler-Lagrange equation maximizes consistency with all of the given video data simultaneously. The result is a 3D model of the scene which varies smoothly over time. The geometry reconstructed by this scheme is significantly better than results obtained by space-carving approaches that do not enforce temporal coherence.