图参数化最优控制问题的指标定理
Index theorems for graph-parametrized optimal control problems
AI总结：
本文针对图上约束变分问题建立Morse指标定理，给出两个Hessian指标差的计算公式，并证明迭代公式与指标下界等应用。
摘要：
本文证明了一类广泛的图上约束变分问题的Morse指标定理。这类定理在多种物理和几何应用中十分有用。我们的公式计算了与两个不同图或两组不同边界条件相关的两个Hessian的Morse指标之差。文中还证明了若干应用，例如迭代公式或指标的下界。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
