论文标题
在liouville方程的非简单爆炸解决方案上
On Non-simple blowup solutions of Liouville equation
论文作者
论文摘要
对于具有量化奇异来源的liouville方程式，多年来，非简单的爆炸现象一直是一个主要困难。前两位作者的猜想是，如果在具有差点边界条件的单位球上定义了方程式，则不会发生非简单爆炸现象。在本文中，我们不仅完全解决了该猜想的整体，而且还扩展了我们的结果以涵盖任何有限的领域。由于本文中的主要定理排除了通常观察到的应用中的非简单现象，因此它可能为学位计数计划的进步，爆炸解决方案的唯一性和解决方案的构建等铺平道路。
For Liouville equation with quantized singular sources, the non-simple blowup phenomenon has been a major difficulty for years. It was conjectured by the first two authors that the non-simple blowup phenomenon does not occur if the equation is defined on the unit ball with Dirichlet boundary condition. In this article we not only completely settle this conjecture in its entirety, but also extend our result to cover any bounded domain. Since the main theorem in this article rules out the non-simple phenomenon in commonly observed applications, it may pave the way for advances in degree counting programs, uniqueness of blowup solutions and construction of solutions, etc.
