A gluing approach for the fractional Yamabe problem with isolated singularities
A gluing approach for the fractional Yamabe problem with isolated singularities
复制标题
具有孤立奇点的分数 Yamabe 问题的粘合方法
DOI：
10.1515/crelle-2018-0032
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发表时间：
2020
影响因子：
1.5
通讯作者：
Wei Juncheng
中科院分区：
文献类型：
--
作者：
Ao Weiwei;DelaTorre Azahara;Gonzalez Maria del Mar;Wei Juncheng
摘要我们构造了分数阶Yamabe问题的解，这些解在给定的孤立点个数处是奇异的。这似乎是第一次成功地将胶合方法应用于非局部问题，以构造奇异解。在证明中有两个主要步骤：通过在每个奇点处胶合半泡罩塔来构造近似解，然后使用无穷维Lyapunov-Schmidt约化方法，将问题约化为（无穷维）Toda型系统。主要技术部分是对鼓泡塔中不同气泡之间相互作用的估计。
Abstract We construct solutions for the fractional Yamabe problem that are singular at a prescribed number of isolated points. This seems to be the first time that a gluing method is successfully applied to a non-local problem in order to construct singular solutions. There are two main steps in the proof: to construct an approximate solution by gluing half bubble towers at each singular point, and then an infinite-dimensional Lyapunov–Schmidt reduction method, that reduces the problem to an (infinite-dimensional) Toda-type system. The main technical part is the estimate of the interactions between different bubbles in the bubble towers.