自由边界极小超曲面的紧致性与一般有限性（一）
微分几何
2021-01-27 v3
摘要
给定一个带边界的紧黎曼流形，我们证明：具有一致面积与上界莫尔斯指数的嵌入（可能非真）自由边界极小超曲面的空间，在远离有限个点的光滑图形收敛意义下是紧致的。我们表明，当极限具有重数一时，此类超曲面序列的极限总是继承一个非平凡的 Jacobi 场。在后续论文中，我们将在收敛具有更高重数时构造 Jacobi 场。
引用
@article{arxiv.1803.01509,
title = {Compactness and generic finiteness for free boundary minimal hypersurfaces (I)},
author = {Qiang Guang and Zhichao Wang and Xin Zhou},
journal= {arXiv preprint arXiv:1803.01509},
year = {2021}
}
备注
We fixed a gap in the construction of Jacobi fields and split the original paper into two parts. The followup paper(the second part) will deal with the construction of Jacobi fields when the convergence has higher multiplicity