Compactness and partial regularity theory of Ricci flows in higher dimensions

Richard Bamler (Berkeley)

09-Mar-2021, 17:00-18:00 (3 years ago)

Abstract: We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow. Under a natural non-collapsing condition, this limiting flow is smooth on the complement of a singular set of parabolic codimension at least 4. We furthermore obtain a stratification of the singular set with optimal dimensional bounds depending on the symmetries of the tangent flows. Our methods also imply the corresponding quantitative stratification result and the expected $L^p$-curvature bounds.

As an application we obtain a description of the singularity formation at the first singular time and a long-time characterization of immortal flows, which generalizes the thick-thin decomposition in dimension 3. We also obtain a backwards pseudolocality theorem and discuss several other applications.

differential geometry

Audience: researchers in the topic


B.O.W.L Geometry Seminar

Organizers: Joel Fine, Lorenzo Foscolo*, Peter Topping
Curators: Jason D Lotay*, Costante Bellettini, Bruno Premoselli, Felix Schulze, Huy The Nguyen, Marco Guaraco, Michael Singer
*contact for this listing

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