Approximate eigen-data on an open subset determine a closed Riemannian manifold up to Lipschitz distance epsilon^(1/12) and a Lipschitz potential up to epsilon^(1/(80n)), giving double-logarithmic stability.
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Stability of Gel'fand's inverse interior spectral problem for Schr\"odinger operators
Approximate eigen-data on an open subset determine a closed Riemannian manifold up to Lipschitz distance epsilon^(1/12) and a Lipschitz potential up to epsilon^(1/(80n)), giving double-logarithmic stability.