A global weak solution to the full bosonic string heat flow
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.
KeywordsFull bosonic string Heat flow Global weak solution
Mathematics Subject Classification58E20 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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