2016/10/09 by Duong H. Phong, D. H. Phong, Sébastien Picard +5 · 3 citations
Mathematics · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP #math.CV #math.DG
paper · pdf · doi:10.48550/arxiv.1610.02740
54 pages; details added
openalex publication_date 2016/10/09 · arxiv created 2018/03/23 · arxiv updated 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The Anomaly flow is shown to converge on toric fibrations with the Fu-Yau ansatz, for both positive and negative values of the slope parameter α'. This implies both results of Fu and Yau on the existence of solutions for Hull-Strominger systems, which they proved using different methods depending on the sign of α'. It is also the first case where the Anomaly flow can even be shown to exist for all time. This is in itself remarkable from the point of view of the theory of fully nonlinear partial differential equations, as the elliptic terms in the flow are not concave.