The scattering matrix for the p-form Laplacian on asymptotically conic manifolds

Nelia Charalambous; Alden Waters

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arXiv · 2608.22984

The scattering matrix for the p-form Laplacian on asymptotically conic manifolds

Nelia Charalambous·Alden Waters

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Abstract

We give an explicit description of the scattering matrix for the Hodge-Laplacian on co-closed p-forms on asymptotically conic manifolds of dimension $n\geq 3$. We develop generalized eigenfunctions and a functional calculus to describe the result, a departure from the Fourier Integral Operators used in the scalar case. Starting from the Hodge decomposition at infinity, we construct generalized eigenforms which are co-closed and establish a spectral representation for the p-form Hodge Laplacian. The special case of dimension 3 for $p=1$ characterises the electric field for Maxwell's equations.

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Nelia Charalambous, Alden Waters. 2026-08-24. The scattering matrix for the p-form Laplacian on asymptotically conic manifolds. https://arxiv.org/abs/2608.22984

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