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A Bernstein result and counterexample for entire solutions to Donaldson's equation


Author: Micah Warren
Journal: Proc. Amer. Math. Soc. 144 (2016), 2953-2958
MSC (2010): Primary 35J60
DOI: https://doi.org/10.1090/proc/12960
Published electronically: October 22, 2015
MathSciNet review: 3487227
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Abstract: We show that convex entire solutions to Donaldson's equation are quadratic, using a result of Weiyong He. We also exhibit entire solutions to the Donaldson equation that are not of the form discussed by He. In the process we discover some nontrivial entire solutions to complex Monge-Ampère equations.


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Micah Warren
Affiliation: Department of Mathematics, University of Oregon, Fenton Hall, Eugene, Oregon 97403
Email: micahw@uoregon.edu

DOI: https://doi.org/10.1090/proc/12960
Received by editor(s): April 10, 2015
Received by editor(s) in revised form: August 20, 2015
Published electronically: October 22, 2015
Additional Notes: The author’s work was supported in part by the NSF via DMS-1161498
Communicated by: Guofang Wei
Article copyright: © Copyright 2015 American Mathematical Society