Paper · Mar 1, 2022
Convergence of the Sasaki-Ricci flow on Sasakian 5-manifolds of general type
As on arXiv
Abstract
In this paper, we show that the uniform L^4-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular Sasakian (2n+1)-manifold M of general type. As an application, any solution of the normalized Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular Sasaki η-Einstein metric on the transverse canonical model M_can of M if n is less than or equal to 3. In particular for n equal to 2, M_can is a S^1-orbibundle over the unique Keahler-Einstein orbifold surface (Z_can,ω_KE) with finite point orbifold singularities. The floating foliation (-2)-curves in M will be contracted to orbifold points by the Sasaki-Ricci flow as t goes to infinite.
Comments: arXiv admin note: text overlap with arXiv:1004.2461, arXiv:1508.04823, arXiv:1212.3653 by other authors
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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.