论文标题
谐波图序列的索引估计
Index estimates for sequences of harmonic maps
论文作者
论文摘要
在本文中，我们研究了指数的上和下边界，以及从二维Riemann表面均匀界定的dirichlet能量的谐波图序列的序列和无效。主要难度源于以下事实：在极限中，序列可以产生有限的气泡。我们通过研究线性操作员征征序列的序列的限制行为以及本文的关键新颖性，即我们将dirichlet能量的指数形式对角线与双线性形式相对于谐波图和谐波序列而变化，这有助于在Eigenformintion eigen -eigenfunctions contressions contressions contressions contriptions and igenections和diriNear形式变化。 最后，我们素描如何修改我们的论点，以涵盖更一般的二维形式不变变量问题的临界点的序列。
In this paper we study upper and lower bounds of the index and the nullity for sequences of harmonic maps with uniformly bounded Dirichlet energy from a two-dimensional Riemann surface into a compact target manifold. The main difficulty stems from the fact that in the limit the sequence can develop finitely many bubbles. We obtain the index bounds by studying the limiting behavior of sequences of eigenfunctions of the linearized operator and the key novelty of the present paper is that we diagonalize the index form of the Dirichlet energy with respect to a bilinear form which varies with the sequence of harmonic maps and which helps us to show the convergence of the sequence of eigenfunctions on the weak limit, the bubbles and the intermediate neck regions. Finally, we sketch how to modify our arguments in order to also cover the more general case of sequences of critical points of two-dimensional conformally invariant variational problems.
