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December  2015, 35(12): 5787-5798. doi: 10.3934/dcds.2015.35.5787

Short-time existence of the second order renormalization group flow in dimension three

Laura Cremaschi 1, and  Carlo Mantegazza 1,

1. 

Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, 56126, Italy, Italy

Received  January 2014 Published  May 2015

Given a compact three--manifold together with a Riemannian metric, we prove the short--time existence of a solution to the renormalization group flow, truncated at the second order term, under a suitable hypothesis on the sectional curvature of the initial metric.
Keywords: evolution equation, Renormalization group, Ricci flow, Riemann tensor, quasilinear PDE..
Mathematics Subject Classification: Primary: 53C44; Secondary: 35K4.
Citation: Laura Cremaschi, Carlo Mantegazza. Short-time existence of the second order renormalization group flow in dimension three. Discrete & Continuous Dynamical Systems, 2015, 35 (12) : 5787-5798. doi: 10.3934/dcds.2015.35.5787
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show all references

References:
[1]

Springer-Verlag, 1998. doi: 10.1007/978-3-662-13006-3.  Google Scholar

[2]

Springer-Verlag, Berlin, 2008.  Google Scholar

[3]

preprint, 2010. Google Scholar

[4]

Proc. Amer. Math. Soc., 134 (2006), 1803-1807 (electronic). doi: 10.1090/S0002-9939-05-08204-3.  Google Scholar

[5]

Milan J. Math., 78 (2010), 319-353. doi: 10.1007/s00032-010-0110-y.  Google Scholar

[6]

Classical Quantum Gravity, 5 (1988), 659-693. doi: 10.1088/0264-9381/5/5/005.  Google Scholar

[7]

Turkish J. Math., 28 (2004), 1-10.  Google Scholar

[8]

Mathematical Surveys and Monographs, 110, American Mathematical Society, Providence, RI, 2004. doi: 10.1090/surv/110.  Google Scholar

[9]

J. Diff. Geom., 18 (1983), 157-162.  Google Scholar

[10]

in Collected Papers on Ricci Flow (eds. H.-D. Cao, B. Chow, S.-C. Chu and S.-T. Yau), Series in Geometry and Topology, 37, Int. Press, 2003, 163-165. Google Scholar

[11]

Amer. J. Math., 86 (1964), 109-160. doi: 10.2307/2373037.  Google Scholar

[12]

Phys. Rev. Lett., 45 (1980), 1057-1060. doi: 10.1103/PhysRevLett.45.1057.  Google Scholar

[13]

Ann. Physics, 163 (1985), 318-419. doi: 10.1016/0003-4916(85)90384-7.  Google Scholar

[14]

Prentice-Hall Inc., Englewood Cliffs, NJ, 1964.  Google Scholar

[15]

Springer-Verlag, 1990. doi: 10.1007/978-3-642-97242-3.  Google Scholar

[16]

J. Fixed Point Theory Appl., 14 (2013), 3-20. doi: 10.1007/s11784-014-0162-7.  Google Scholar

[17]

Comm. Anal. Geom., 21 (2013), 435-467. doi: 10.4310/CAG.2013.v21.n2.a7.  Google Scholar

[18]

preprint, 2014. Google Scholar

[19]

Lett. Math. Phys., 84 (2008), 149-157. doi: 10.1007/s11005-008-0245-8.  Google Scholar

[20]

J. Diff. Geom., 17 (1982), 255-306.  Google Scholar

[21]

Nuclear Phys. B, 322 (1989), 431-470. doi: 10.1016/0550-3213(89)90422-7.  Google Scholar

[22]

Comm. Math. Phys., 107 (1986), 165-176. doi: 10.1007/BF01206956.  Google Scholar

[23]

Ann. Sc. Norm. Sup. Pisa, 11 (2012), 857-874.  Google Scholar

[24]

Classical Quantum Gravity, 26 (2009), 105020, 8pp. doi: 10.1088/0264-9381/26/10/105020.  Google Scholar

[25]

Phys. Rev. D, 76 (2007), 045001, 7pp. doi: 10.1103/PhysRevD.76.045001.  Google Scholar

[26]

London Mathematical Society Lecture Note Series, 325, Cambridge University Press, Cambridge, 2006. doi: 10.1017/CBO9780511721465.  Google Scholar

[27]

Phys. Rev. D, 75 (2007), 064024, 6pp. doi: 10.1103/PhysRevD.75.064024.  Google Scholar

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