Reconstructing currents from their projections

We prove an inversion formula for the exterior $k$-plane transform. As a consequence, we show that if $m < k$ then an $m$-current in $\mathbf R^n$ can be reconstructed from its projections onto $\mathbf R^k$, which proves a conjecture of Solomon.

Publication Details

Journal
ArXiv.org
Published
2025-03-10
Primary Topic
Mathematical Analysis and Transform Methods
Type
article
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article

Reconstructing currents from their projections

ArXiv.org
Mathematical Analysis and Transform Methods
article

Reconstructing currents from their projections

article en

Abstract

We prove an inversion formula for the exterior $k$-plane transform. As a consequence, we show that if $m < k$ then an $m$-current in $\mathbf R^n$ can be reconstructed from its projections onto $\mathbf R^k$, which proves a conjecture of Solomon.

ArXiv.org
Openalex Percentile: Top 40%
Mathematical Analysis and Transform Methods
Open Access PDFOpenAlex
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Reconstructing currents from their projections · ArXiv.org (2025) | TGRS Research Map | TGRS