欧几里得体积增长黎曼流形上的尖锐估计与不等式
偏微分方程分析
2025-10-07 v2 微分几何
摘要
我们获得了具有欧几里得体积增长和非负Ricci曲率的完备非紧黎曼流形上热核和格林函数的尖锐估计。随后，我们将这些估计应用于此类流形上的Moser-Trudinger不等式，得到了尖锐形式。
引用
@article{arxiv.2412.05638,
title = {Sharp estimates and inequalities on Riemannian manifolds with Euclidean volume growth},
author = {Luigi Fontana and Carlo Morpurgo and Liuyu Qin},
journal= {arXiv preprint arXiv:2412.05638},
year = {2025}
}
备注
38 pages. In v.2 sharpness statements were added in Theorem 1 and Theorem 2. Section 6, containing the proofs of such statements, was revised accordingly. Several comments were added after the statement of Theorem 2. Few minor revisions and corrections