This paper studies the interplay between the concepts of error bounds and the Kurdyka–Łojasiewicz (KL) inequality on Hadamard manifolds. To this end, we extend some properties and existence results of a solution for differential inclusions on Hadamard manifolds. As a second contribution, we show how the KL inequality can be used to obtain the convergence of the gradient method for solving convex feasibility problems on Hadamard manifolds. The convergence results of the alternating projection method are also established for cyclic and random projections on Hadamard manifolds and, more generally, CAT(0) spaces.

中文翻译：

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哈达玛流形上 Kurdyka-Łojasiewicz 性质与误差界的关系

本文研究了哈达玛流形上误差界概念与 Kurdyka-Łojasiewicz (KL) 不等式之间的相互作用。为此，我们扩展了 Hadamard 流形上微分包含解的一些性质和存在性结果。作为第二个贡献，我们展示了如何使用 KL 不等式来获得梯度法的收敛性，以解决 Hadamard 流形上的凸可行性问题。交替投影方法的收敛结果也适用于 Hadamard 流形以及更一般的 CAT(0) 空间上的循环和随机投影。