具有极大体积增长的Calabi-Yau流形上的次二次调和函数
微分几何
2024-10-24 v2
摘要
在具有极大体积增长的完备Calabi-Yau流形上，具有次二次多项式增长的调和函数是某个全纯函数实部。这推广了Conlon-Hein的结果。我们通过证明调和-形式的Liouville型定理来证明该结果，而后者源于对外导数新的局部估计。
引用
@article{arxiv.1905.12965,
title = {Subquadratic harmonic functions on Calabi-Yau manifolds with maximal volume growth},
author = {Shih-Kai Chiu},
journal= {arXiv preprint arXiv:1905.12965},
year = {2024}
}
备注
24 pages. Second proof of main result removed; various improvements based on Referees' suggestions