Abstract
We prove the existence of a unique global weak solution to the full bosonic string heat flow from closed Riemannian surfaces to an arbitrary target under smallness conditions on the two-form and the scalar potential. The solution is smooth with the exception of finitely many singular points. Finally, we discuss the convergence of the heat flow and obtain a new existence result for critical points of the full bosonic string action.
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Acknowledgements
Open access funding provided by University of Vienna. The author gratefully acknowledges the support of the Austrian Science Fund (FWF) through the START-Project Y963-N35 of Michael Eichmair and the Project P30749-N35 “Geometric variational problems from string theory.”
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Branding, V. A global weak solution to the full bosonic string heat flow. J. Evol. Equ. 18, 1819–1841 (2018). https://doi.org/10.1007/s00028-018-0462-2
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DOI: https://doi.org/10.1007/s00028-018-0462-2