Geometry & Topology

The uniqueness of tangent flows is central to understanding singularity formation in geometric flows. A foundational result of Colding and Minicozzi establishes this uniqueness at cylindrical singularities under the Type I assumption in the Ricci flow. In this talk, I will present a strong uniqueness result for cylindrical tangent flows at the first singular time. Our proof hinges on a Łojasiewicz inequality for the pointed $\mathcal{W}$-entropy, which is established under the assumption that the local geometry near the base point is close to a standard cylinder or its quotient. This is joint work with Yu Li.