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arXiv · 2310.14020

Dimension Reduction for Positively Curved Steady Solitons

Pak-Yeung Chan·Zilu Ma·Yongjia Zhang
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Abstract

We consider noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature. We show that such solitons always dimension reduce at infinity. This generalizes an earlier result in [CDM22] to higher dimensions. In dimension four, we classify possible reductions at infinity, which lays foundation for possible classifications of steady solitons. Moreover, we show that any tangent flow at infinity of a general noncollapsed steady soliton must split off a line. This generalizes an earlier result in [BCDMZ21] to higher dimensions. While this article is under preparation, we realized that part of our main results are proved independently in a recent post [ZZ23] under different assumptions.

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Pak-Yeung Chan, Zilu Ma, Yongjia Zhang. 2023-10-21. Dimension Reduction for Positively Curved Steady Solitons. https://arxiv.org/abs/2310.14020

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