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Short-time existence for the second order renormalization group flow in general dimensions


Authors: Karsten Gimre, Christine Guenther and James Isenberg
Journal: Proc. Amer. Math. Soc. 143 (2015), 4397-4401
MSC (2010): Primary 53C44
DOI: https://doi.org/10.1090/proc/12457
Published electronically: June 9, 2015
MathSciNet review: 3373938
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Abstract: We prove local existence for the second order Renormalization Group flow initial value problem on closed Riemannian manifolds $ (M,g)$ in general dimensions, for initial metrics whose sectional curvatures $ K_\pi $ satisfy the condition $ 1+\alpha K_\pi > 0$, at all points $ p \in M$ and for all planes $ \pi \subset T_p M$. This extends results previously proven for two and three dimensions.


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Additional Information

Karsten Gimre
Affiliation: Department of Mathematics, Columbia University, New York City, New York 10027
Email: gimre@math.columbia.edu

Christine Guenther
Affiliation: Department of Mathematics and Computer Science, Pacific University, Forest Grove, Oregon 97116
Email: guenther@pacificu.edu

James Isenberg
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: isenberg@uoregon.edu

DOI: https://doi.org/10.1090/proc/12457
Received by editor(s): January 7, 2014
Published electronically: June 9, 2015
Additional Notes: The first author was partially supported by the NSF under grant DGE-1144155.
The second author was partially supported by the Simons Foundation Collaboration Grant for Mathematicians - 283083
The third author was partially supported by the NSF under grant PHY-1306441 at the University of Oregon. He also wishes to thank the Mathematical Sciences Research Institute in Berkeley, California, for support under grant 0932078 000. Some of this work was carried out while the third author was in residence at MSRI during the fall of 2013.
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society