关于稳定梯度利玛窦孤子的标量曲率下界的说明

arXiv - MATH - Differential Geometry Pub Date : 2024-09-01 DOI:arxiv-2409.00583

Shota Hamanaka

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引用次数: 0

摘要

我们为稳梯度里奇孤子的标量曲率提供了新型衰减估计。我们还给出了$\infty$-Bakry--Emery Ricci张量自下而上以某个正常数为界的黎曼流形的直径上限。为了证明这一点，我们使用了格罗莫夫引入的$\mu$气泡。

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Notes on scalar curvature lower bounds of steady gradient Ricci solitons

We provide new type of decay estimate for scalar curvatures of steady gradient Ricci solitons. We also give certain upper bound for the diameter of a Riemannian manifold whose $\infty$-Bakry--Emery Ricci tensor is bounded by some positive constant from below. For the proofs, we use $\mu$-bubbles introduced by Gromov.

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arXiv - MATH - Differential Geometry

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