2024/03/09 by Bohr, Jan, Monard, François, Paternain, Gabriel P. · 1 citation
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2403.05985
Transport twistor spaces are degenerate complex 2-dimensional manifolds Z that complexify transport problems on Riemannian surfaces, appearing e.g.~in geometric inverse problems. This article considers maps β\colon Z→ ℂ2 with a holomorphic blow-down structure that resolve the degeneracy of the complex structure and allow to gain insight into the complex geometry of Z. The main theorems provide global β-maps for constant curvature metrics and their perturbations and local β-maps for arbitrary metrics, thereby proving a version of the classical Newlander--Nirenberg theorem for degenerate complex structures.