English

The Anomaly flow over Riemann surfaces

Differential Geometry 2021-11-30 v1 High Energy Physics - Theory Analysis of PDEs Complex Variables

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 threefold.

Keywords

Cite

@article{arxiv.1711.08186,
  title  = {The Anomaly flow over Riemann surfaces},
  author = {Teng Fei and Zhijie Huang and Sebastien Picard},
  journal= {arXiv preprint arXiv:1711.08186},
  year   = {2021}
}

Comments

22 pages

R2 v1 2026-06-22T22:53:43.722Z