论文标题
在带有约束的摩尔斯指数上：抽象的表述
On the Morse Index with Constraints I: An Abstract Formulation
论文作者
论文摘要
在此序列中，我们首先证明了希尔伯特空间中抽象的摩尔斯索引定理，该定理对约束的变异问题建模。然后，我们的抽象公式用于研究几种优化设置，包括封闭的CMC Hypersurfaces，球中的毛细管表面以及II型分区的临界点。在本文中，我们研究了希尔伯特空间中对称界的双线性形式的指数和无效。主要结果确切地决定了这些概念在限制有限的编成子空间时的变化。
In this sequence, we first prove an abstract Morse index theorem in a Hilbert space modeling a variational problem with constraints. Then, our abstract formulation is applied to study several optimization setups including closed CMC hypersurfaces, capillary surfaces in a ball, and critical points of type-II partitioning. In this paper, we study the index and nullity of a symmetric bounded bilinear form in a Hilbert space. The main results determine precisely how these notions change when restricting to a subspace of a finite codimension.
