论文标题
涉及紧凑式Riemann表面边界上等温坐标的爆破分析
Blow-up analysis involving isothermal coordinates on the boundary of compact Riemann surface
论文作者
论文摘要
使用爆破分析方法，我们在紧凑的黎曼表面上获得了两个尖锐的特鲁丁格 - 摩萨剂不等式，并具有光滑的边界，以及相应的极端物体的存在。这概括了Chang-Yang [7]和第一个命名作者[32]的早期结果，并补充了Fontana对二维的不平等[15]。当前论文中的爆炸分析要比[32]的爆炸性得多得多，并且特别阐明了那里的几个模棱两可的观点。从确切地说，我们证明了边界附近的等温坐标系统的存在，绿色功能的存在和均匀的估计值，具有Neumann边界条件。另外，我们的分析可以应用于卡兹丹 - 瓦纳（Kazdan-Warner）问题和Chern-simons Higgs问题，这些问题在紧凑的riemman表面上具有光滑的边界。
Using the method of blow-up analysis, we obtain two sharp Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary, as well as the existence of the corresponding extremals. This generalizes early results of Chang-Yang [7] and the first named author [32], and complements Fontana's inequality of two dimensions [15]. The blow-up analysis in the current paper is far more elaborate than that of [32], and particularly clarifies several ambiguous points there. In precise, we prove the existence of isothermal coordinate systems near the boundary, the existence and uniform estimates of the Green function with the Neumann boundary condition. Also our analysis can be applied to the Kazdan-Warner problem and the Chern-Simons Higgs problem on compact Riemman surfaces with smooth boundaries.
