从具有非负Ricci曲率的流形出发的能量极小映射
微分几何
2025-04-24 v3
摘要
从具有非负Ricci曲率的紧致连通黎曼流形到无共轭点的完备黎曼流形的一个同伦类映射的任意代表的能量，被由目标流形的渐近几何所决定的常数从下方界定，且等号成立当且仅当原映射为全测地映射。这一结论在更弱的假设下也成立：即定义域被一个微分同胚乘积有限覆盖，且其万有覆盖空间等距分裂为一个带平坦因子的乘积，这由Cheeger-Gromoll分裂定理导出的交换图所刻画。
引用
@article{arxiv.1805.07701,
title = {Energy-minimizing maps from manifolds with nonnegative Ricci curvature},
author = {James Dibble},
journal= {arXiv preprint arXiv:1805.07701},
year = {2025}
}
备注
17 pages; corrected an error in the statement of Lemma 2.3 and a minor error in inequality (3.10); removed mention of "manifolds with corners" from the proof of inequality (3.9); edited for style and clarity throughout