Abstract We present some estimate of the Laplacian Spectrum and of Topological Invariants for Riemannian manifold with pinched sectional curvature and with non-empty and non-convex boundary with finite injectivity radius. These estimates do not depend directly on the the lower bound of the boundary injectivity radius but on the bounds of the curvatures of the manifold and its boundary.

中文翻译：

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具有边界 II 的黎曼流形的拉普拉斯谱和拓扑不变量边界的估计

摘要 我们提出了一些关于拉普拉斯谱和黎曼流形的拓扑不变量的估计，该流形具有收缩截面曲率和具有有限注入半径的非空和非凸边界。这些估计不直接取决于边界注入半径的下限，而是取决于流形及其边界的曲率边界。