Paper · Oct 23, 2025
Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow
As on arXiv
Abstract
In this paper, we establish a Lojasiewicz inequality for the pointed -entropy in the Ricci flow, under the assumption that the geometry near the base point is close to a standard cylinder or the quotient thereof. As an application, we prove the strong uniqueness of the cylindrical tangent flow at the first singular time of the Ricci flow. Specifically, we show that the modified Ricci flow near the singularity converges to the cylindrical model under a fixed gauge.
Comments: Minor improvement to the decay rate in the main result. 93 pages. Comments are welcome!
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow
Topics Singularities, Stability & uniqueness · Same authors Hanbing Fang, Yu Li · Shared terms “strong uniqueness”, “cylindrical singularities”, “Lojasiewicz inequality”
-
On the geometry of asymptotically conical Ricci shrinkers (II): strong uniqueness
Topics Singularities, Stability & uniqueness · Same author Yu Li · Shared terms “strong uniqueness”, “fixed gauge”, “tangent flow”
-
Singular sets in noncollapsed Ricci flow limit spaces
Topics Singularities · Same authors Hanbing Fang, Yu Li · Shared terms “tangent flow”, “standard cylinder”, “quotient”
-
On the rigidity of Ricci shrinkers
Topics Singularities, Stability & uniqueness · Same author Yu Li · Shared terms “tangent flow”, “quotient thereof”
-
Cylindrical tangent flows in mean curvature flow
Topics Singularities, Stability & uniqueness · Shared terms “cylindrical singularities”, “cylindrical tangent”, “tangent flow”
-
On the structure of noncollapsed Ricci flow limit spaces
Topics Ricci flow · Same authors Hanbing Fang, Yu Li
-
On the tangent flows of noncollapsed Ricci flow limit spaces
Topics Singularities · Same author Yu Li · Shared terms “tangent flow”
-
Volume estimates for the singular sets of mean curvature flows
Same authors Hanbing Fang, Yu Li
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11B.4Blow-Ups, Blow-Downs and Splitting at Infinity
Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.
- 11B.6Rotationally Symmetric Flows and the Standard Solution
The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.
- 6A.13Self-Similar Variables and Monotonicity
Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.