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arXiv · 2208.00454

An inverse problem for fractional connection Laplacians

Chun-Kai Kevin Chien
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Abstract

Consider a fractional operator $P^s$, $0<s<1$, for connection Laplacian $P:=\nabla^*\nabla+A$ on a smooth Hermitian vector bundle over a closed, connected Riemannian manifold of dimension $n\geq 2$. We show that local knowledge of the metric, Hermitian bundle, connection, potential, and source-to-solution map associated with $P^s$ determines these structures globally. This extends a result known for the fractional Laplace-Beltrami operator.

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Chun-Kai Kevin Chien. 2022-07-31. An inverse problem for fractional connection Laplacians. https://arxiv.org/abs/2208.00454

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