Journal of Evolution Equations

, Volume 18, Issue 4, pp 1819–1841 | Cite as

A global weak solution to the full bosonic string heat flow

  • Volker BrandingEmail author
Open Access


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.


Full bosonic string Heat flow Global weak solution 

Mathematics Subject Classification

58E20 35K55 53C80 



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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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria

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