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.
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