The Anomaly flow over Riemann surfaces

Teng Fei; Zhijie Huang; Sebastien Picard

doi:10.1093/imrn/rnz076

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arXiv · 1711.08186

The Anomaly flow over Riemann surfaces

Teng Fei·Zhijie Huang·Sebastien Picard

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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.

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BibTeX RIS

Teng Fei, Zhijie Huang, Sebastien Picard. 2017-11-22. The Anomaly flow over Riemann surfaces. https://doi.org/10.1093/imrn%2Frnz076

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