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Global viscosity solutions of generalized Kähler-Ricci flow

Author: Jeffrey Streets
Journal: Proc. Amer. Math. Soc. 146 (2018), 747-757
MSC (2010): Primary 53C44, 35D40
Published electronically: August 30, 2017
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Abstract: We apply ideas from viscosity theory to establish the existence of a unique global weak solution to the generalized Kähler-Ricci flow in the setting of commuting complex structures. Our results are restricted to the case of a smooth manifold with smooth background data. We discuss the possibility of extending these results to more singular settings, pointing out a key error in the existing literature on viscosity solutions to complex Monge-Ampère equations/Kähler-Ricci flow.

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Jeffrey Streets
Affiliation: Department of Mathematics, Rowland Hall, University of California, Irvine, Irvine, California 92617

Received by editor(s): October 6, 2016
Received by editor(s) in revised form: March 22, 2017
Published electronically: August 30, 2017
Additional Notes: The author gratefully acknowledges support from the NSF via DMS-1454854, and from an Alfred P. Sloan Fellowship.
Communicated by: Lei Ni
Article copyright: © Copyright 2017 American Mathematical Society

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