论文标题
用规定的高斯和大地曲面的磁盘的共形指标进行爆破分析
Blow-up analysis of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures
论文作者
论文摘要
本文与规定的高斯和大地曲线相关的磁盘指标的紧凑性。我们考虑了一个爆炸的指标序列，并对其渐近行为进行了精确描述。特别是，指标在边界上的独特点上爆炸，我们能够在其位置提供必要的条件。事实证明，这种条件在局部取决于高斯曲线，但它们以非本地的方式取决于测地曲线。这是关于爆炸条件是局部的经典尼伦贝格问题的新颖性，而这一新方面是由边界条件驱动的。
This paper is concerned with the compactness of metrics of the disk with prescribed Gaussian and geodesic curvatures. We consider a blowing-up sequence of metrics and give a precise description of its asymptotic behavior. In particular, the metrics blow-up at a unique point on the boundary and we are able to give necessary conditions on its location. It turns out that such conditions depend locally on the Gaussian curvatures but they depend on the geodesic curvatures in a nonlocal way. This is a novelty with respect to the classical Nirenberg problem where the blow-up conditions are local, and this new aspect is driven by the boundary condition.
