On uniqueness of tangent cones for Einstein manifolds

• 成果类型: Article
• 署名作者: Colding, Tobias Holck; Minicozzi, William P., II
• 署名单位: Massachusetts Institute of Technology (MIT); Johns Hopkins University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0474-z
• 发表日期: 2014
• 页码: 515-588
• 关键词: ricci curvature; BEHAVIOR; SPACES; bounds

摘要

We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section.