论文标题
关键点的摩尔斯索引稳定性，即形式不变的Lagrangians
Morse Index Stability for Critical Points to Conformally invariant Lagrangians
论文作者
论文摘要
我们证明了莫尔斯指数的上层含量，以及在弱收敛下维度2中普遍不变的拉格朗日人的关键点的无效。确切地确定，莫尔斯指标的总和和任意依赖的任意序列无效的临界点到一般的子孙来来说，将临界点从任意封闭的表面从任意封闭的表面到任意封闭的平滑流行段到一个限制的一般形式不变的拉格朗日，以下是不限制的，而莫尔斯的莫尔斯的总和是不限制的。弱极限与气泡的摩尔斯指数的索引是由弱收敛序列的摩尔斯指数渐近地界定的。然后，主要结果将扩展到从域序列序列的情况下扩展到域的序列，从而假设与该变性相关的项圈的图像长度保持在临界长度以下。
We prove the upper-semi-continuity of the Morse index plus nullity of critical points to general conformally invariant Lagrangians in dimension 2 under weak convergence. Precisely we establish that the sum of the Morse indices and the nullity of an arbitrary sequence of weakly converging critical points to a general conformally invariant Lagrangians of maps from an arbitrary closed surface into an arbitrary closed smooth manifold passes to the limit in the following sense : it is asymptotically bounded from above by the sum of the Morse indices plus the nullity of the weak limit and the bubbles, while it was well known that the sum of the Morse index of the weak limit with the Morse indices of the bubbles is asymptotically bounded from above by the Morse indices of the weakly converging sequence. The main result is then extended to the case of sequences of maps from sequences of domains degenerating to a punctured Riemann surface assuming that the lengths of the images by the maps of the collars associated to this degeneration stay below some critical length.
