Paper · Mar 24, 2022
Complete gradient expanding Ricci solitons with finite asymptotic scalar curvature ratio
As on arXiv
Abstract
Let , , be a complete gradient expanding Ricci soliton with nonnegative Ricci curvature . In this paper, we show that if the asymptotic scalar curvature ratio of is finite (i.e., ), then the Riemann curvature tensor must have at least sub-quadratic decay, namely, for any .
Comments: 20 pages. Lemma 3.1 statement simplified; the proof of Lemma 3.2 & Lemma 3.3 streamlined. arXiv admin note: text overlap with arXiv:2111.09848
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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
- 6C.4The Yamabe Problem and Critical Exponents
Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.
- 9B.6Scalar Curvature and Topology
Positive scalar curvature, its obstructions, and the positive mass theorem.
- 11B.1Ricci Solitons
Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.