论文标题
关于单数liouville型方程解决方案解决方案解决方案解决方案的爆破分析
On the blow-up analysis at collapsing poles for solutions of singular Liouville type equations
论文作者
论文摘要
我们分析了涉及“崩溃”杆的dirac措施的liouville型方程的爆炸序列。我们考虑到爆炸恰好发生在杆子合并的情况下。 在证明“量化”属性仍然具有“爆炸质量”之后，当爆炸量最小的质量发生时，我们将获得精确的点估计。 有趣的是，当忽略“崩溃”狄拉克措施时，这种估计表达了“常规” liouville方程“泡泡”解决方案获得的确切类似物。这些信息将用于描述Goncalves和Uhlenbeck（2007）引入的Donaldson功能最小化的渐近行为，从而屈服于平均曲率1-凹入到双曲线3个字节中。
We analyse a blow-up sequence of solutions for Liouville type equations involving Dirac measures with "collapsing" poles. We consider the case where blow-up occurs exactly at a point where the poles coalesce. After proving that a "quantization" property still holds for the "blow-up mass", we obtain precise point-wise estimates when blow-up occurs with the least blow-up mass. Interestingly, such estimates express the exact analogue of those obtained for "bubble" solutions of "regular" Liouville equations, when the "collapsing" Dirac measures are neglected. Such information will be used to describe the asymptotic behaviour of minimizers of the Donaldson functional introduced by Goncalves and Uhlenbeck (2007), yielding to mean curvature 1-immersions of surfaces into hyperbolic 3-manifolds.
