Abstract On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah–Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.

中文翻译：

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局部边界条件扰动下 Atiyah-Singer Dirac 算子的 Riesz 连续性

摘要 在具有光滑紧致边界的光滑完整黎曼自旋流形上，我们证明了 Atiyah-Singer Dirac 算子在局部边界条件的扰动下连续依赖于 Riesz 映射的 Lipschitz 界取决于 Ricci 曲率和边界的 Lipschitz 平滑度和椭圆度它的一阶导数以及远离边界紧凑邻域的注入半径的下限。更一般地说，我们证明了具有局部边界条件的流形上椭圆算子函数演算的扰动估计。