A global weak solution to the full bosonic string heat flow
- 52 Downloads
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.”
- 11.Joseph Polchinski. String theory. Vol. I. Cambridge Monographs on Mathematical Physics. An introduction to the bosonic string. Cambridge University Press, Cambridge, 2005 Reprint of the 2003 edition.Google Scholar
- 14.Michael Struwe. Variational methods . Applications to nonlinear partial differential equations and Hamiltonian systems. Springer-Verlag, Berlin, 1990Google Scholar
- 15.Michael Struwe. Variational methods, volume 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. fourth edition, 2008. Applications to nonlinear partial differential equations and Hamiltonian systems. Springer-Verlag, BerlinGoogle Scholar
- 16.Michael E. Taylor. Partial differential equations III. Nonlinear equations, volume 117 of Applied Mathematical Sciences. Springer, New York, second edition, 2011.Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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.