带边界的三维流形上标量平坦度量的紧性定理
微分几何
2019-04-24 v2 偏微分方程分析
摘要
设 (M,g) 为带边界的紧致黎曼三维流形。我们证明了在 g 的共形类中且以边界为常平均曲率超曲面的标量平坦度量集合的紧性。这涉及边界上具有临界 Sobolev 指数的 Yamabe 型方程的爆破分析。
引用
@article{arxiv.1807.08406,
title = {A compactness theorem for scalar-flat metrics on 3-manifolds with boundary},
author = {Sergio Almaraz and Olivaine S. de Queiroz and Shaodong Wang},
journal= {arXiv preprint arXiv:1807.08406},
year = {2019}
}
备注
Final version, to appear in the Journal of Functional Analysis. arXiv admin note: text overlap with arXiv:0906.0927