التفاصيل البيبلوغرافية
| العنوان: |
Stability in the Inverse Steklov Problem on Warped Product Riemannian Manifolds. |
| المؤلفون: |
Daudé, Thierry, Kamran, Niky, Nicoleau, François |
| المصدر: |
Journal of Geometric Analysis; Feb2021, Vol. 31 Issue 2, p1821-1854, 34p |
| مستخلص: |
In this paper, we study the amount of information contained in the Steklov spectrum of some compact manifolds with connected boundary equipped with a warped product metric. Examples of such manifolds can be thought of as deformed balls in R d . We first prove that the Steklov spectrum determines uniquely the warping function of the metric. We show in fact that the approximate knowledge (in a given precise sense) of the Steklov spectrum is enough to determine uniquely the warping function in a neighbourhood of the boundary. Second, we provide stability estimates of log-type on the warping function from the Steklov spectrum. The key element of these stability results relies on a formula that, roughly speaking, connects the inverse data (the Steklov spectrum) to the Laplace transform of the difference of the two warping factors. [ABSTRACT FROM AUTHOR] |
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