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arXiv · 2110.04661

An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons

Richard H. Bamler·Pak-Yeung Chan·Zilu Ma·Yongjia Zhang
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Abstract

In this paper, we prove a volume growth estimate for steady gradient Ricci solitons with bounded Nash entropy. We show that such a steady gradient Ricci soliton has volume growth rate no smaller than $r^{\frac{n+1}{2}}.$ This result not only improves the estimate in [CMZ21b, Theorem 1.3], but also is optimal since the Bryant soliton and Appleton's solitons [Ap17] have exactly this growth rate.

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Richard H. Bamler, Pak-Yeung Chan, Zilu Ma, Yongjia Zhang. 2021-10-09. An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons. https://arxiv.org/abs/2110.04661

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