Griffiths 共轭在紧黎曼曲面上的解析证明
微分几何
2025-12-25 v2
摘要
Griffiths 共轭断言：满射向量束若且仅若其具正曲率的 Hermitian 度量。本文采用 Demailly 引入的偏微分方程系统，对紧黎曼曲面上的该共轭作出新证明。我们的论证结合了 Uhlenbeck-Yau 关于 Hermitian-Einstein 度量的技术与 Pingali 将问题归约为先验估计的方法。
关键词
引用
@article{arxiv.2509.23201,
title = {An analytic proof of Griffiths' conjecture on compact Riemann surfaces},
author = {Rei Murakami},
journal= {arXiv preprint arXiv:2509.23201},
year = {2025}
}
备注
Accepted version. Minor revisions: corrected an issue in the argument, clarified the statement of the main theorem, fixed typos, and added a brief remarks section at the end of the paper. 12 pages