由 q-微分诱导的平坦度量的长度谱
几何拓扑
2018-11-16 v2
摘要
当曲面上的几何结构由曲线的长度决定时，自然会问：我们真正需要知道哪些曲线的长度？Duchin--Leininger--Rafi 的一个结果是，任何由单位范数二次微分诱导的平坦度量由其标记简单长度谱决定。我们将简单曲线的概念推广到 q-简单曲线，对任意正整数 q，并证明 q-简单曲线的长度足以决定由 q-微分诱导的非正曲率欧氏锥度量。
引用
@article{arxiv.1810.01793,
title = {Length spectra of flat metrics coming from q-differentials},
author = {Marissa Loving},
journal= {arXiv preprint arXiv:1810.01793},
year = {2018}
}
备注
An error in the proof of Proposition 3.2 (which is split between the proofs of Lemma 3.1 and 3.2) in the case that q is even has been corrected. The changes involve a slight modification of Definition 3.1 and a short paragraph at the end of each of the proofs of Lemmas 3.1 and 3.2