论文标题
用于图形术的最佳控制问题的索引定理
Index theorems for graph-parametrized optimal control problems
论文作者
论文摘要
在本文中，我们证明了莫尔斯索引定理，用于图形上一系列有限的变分问题。此类定理在各种物理和几何应用中都有用。我们的公式计算了两个与两个不同图或两个不同边界条件集有关的Hessians的Morse指数的差异。证明了几种诸如迭代公式或索引的下限的应用程序。
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two Hessians related to two different graphs or two different sets of boundary conditions. Several applications such as the iteration formulas or lower bounds for the index are proved.
