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arXiv · 2503.21944

Inverse problems for the Bakry-\'Emery Laplacian on manifolds with boundary -- uniqueness and non-uniqueness

Jack Borthwick·Niky Kamran
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Abstract

We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-\'Emery Laplacian $-\Delta_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary $(\overline{M},g)$, endowed with a volume form $\mathfrak{m}=e^{-V}\omega_g$. These consist in recovering the Taylor coefficients of metric $g$ and weight $V$ along the boundary of $\overline{M}$ from the knowledge of a pair of operators that can be viewed as geometrically natural Dirichlet-to-Neumann maps associated to $-\Delta_{\mathcal E}$.

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Jack Borthwick, Niky Kamran. 2025-03-27. Inverse problems for the Bakry-\'Emery Laplacian on manifolds with boundary -- uniqueness and non-uniqueness. https://arxiv.org/abs/2503.21944

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