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An optimal volume growth estimate for noncollapsed steady gradient Ricci solitons
- Publication Year :
- 2021
-
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.<br />Comment: 11 pages
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2110.04661
- Document Type :
- Working Paper