Inverse Spectral Problems for Collapsing Manifolds II: Quantitative Stability of Reconstruction for Orbifolds
arxiv(2024)
摘要
We consider the inverse problem of determining the metric-measure structure
of collapsing manifolds from local measurements of spectral data. In the part I
of the paper, we proved the uniqueness of the inverse problem and a continuity
result for the stability in the closure of Riemannian manifolds with bounded
diameter and sectional curvature in the measured Gromov-Hausdorff topology. In
this paper we show that when the collapse of dimension is 1-dimensional, it
is possible to obtain quantitative stability of the inverse problem for
Riemannian orbifolds. The proof is based on an improved version of the
quantitative unique continuation for the wave operator on Riemannian manifolds
by removing assumptions on the covariant derivatives of the curvature tensor.
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