具有多项式增长右端项的 Monge-Ampère 方程
偏微分方程分析
2024-06-04 v2 微分几何
摘要
我们研究了具有多项式增长右端项的二维 Monge-Ampère 方程解的正则性与增长率。利用这一分析，我们证明了 Gauss 曲率次仿射临界幂流的平移子是光滑且严格凸的整图。这些图展现出仅依赖于流的幂次的具体增长率。
引用
@article{arxiv.2404.01040,
title = {Monge-Amp\`ere equations with right-hand sides of polynomial growth},
author = {Beomjun Choi and Kyeongsu Choi and Soojung Kim},
journal= {arXiv preprint arXiv:2404.01040},
year = {2024}
}
备注
A part of this work was introduced in arXiv:2104.13186v1; however, we have separated and further elaborated the result to accommodate issues that will be dealt in the revision of arXiv:2104.13186. In v2, we generalized the main theorems slightly so that they apply for broader class of equations