From CT scans to 4-manifold topology
Abstract
In this survey paper the ultrahyperbolic equation in dimension four is discussed from a geometric, analytic and topological point of view. The geometry centres on the canonical neutral metric on the space of oriented geodesics of 3-dimensional space-forms, the analysis discusses a mean value theorem for solutions of the equation and presents a new solution of the Cauchy problem over a certain family of null hypersurfaces, while the topology relates to generalizations of codimension two foliations of 4-manifolds.
Cite
@article{arxiv.2309.14826,
title = {From CT scans to 4-manifold topology},
author = {Brendan Guilfoyle},
journal= {arXiv preprint arXiv:2309.14826},
year = {2023}
}
Comments
26 pages, 3 figures. Results from the following papers on arXiv are discussed: 2304.05702, 2204.13163, 2210.08155, 2011.11330, 2110.03998, 1812.03562, 1812.00710, 2002.12787, 1812.00707, 1605.09576, 1404.5509, 0808.0851, math/0702276, math/0407490, math/0406185, 1207.5994, 0709.2441, 1806.05440, 0911.2602