The Anomaly Flow over Riemann Surfaces. (9th April 2019)

• Record Type: Journal Article
• Authors: Fei, Teng; Huang, Zhijie; Picard, Sebastien
• Is Part Of: International mathematics research notices. Volume 2021:Number 3(2021)
• Page Start: 2134
• Page End: 2165
• Publication Date: 2019-04-09
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnz076
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We initiate the study of a new nonlinear parabolic equation on a Riemann surface. The evolution equation arises as a reduction of the Anomaly flow on a fibration. We obtain a criterion for long-time existence for this flow, and give a range of initial data where a singularity forms in finite time, as well as a range of initial data where the solution exists for all time. A geometric interpretation of these results is given in terms of the Anomaly flow on a Calabi–Yau three-fold.