A Bernstein result and counterexample for entire solutions to Donaldson’s equation
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- by Micah Warren PDF
- Proc. Amer. Math. Soc. 144 (2016), 2953-2958 Request permission
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.References
- Simon K. Donaldson, Nahm’s equations and free-boundary problems, The many facets of geometry, Oxford Univ. Press, Oxford, 2010, pp. 71–91. MR 2681687, DOI 10.1093/acprof:oso/9780199534920.003.0005
- Weiyong He, Entire solutions of Donaldson’s equation, Pacific J. Math. 256 (2012), no. 2, 359–363. MR 2944980, DOI 10.2140/pjm.2012.256.359
- Micah Warren, Non-polynomial entire solutions to $\sigma _k$ equations, arXiv:1503.06843.
Additional Information
- Micah Warren
- Affiliation: Department of Mathematics, University of Oregon, Fenton Hall, Eugene, Oregon 97403
- MR Author ID: 842915
- Email: micahw@uoregon.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2953-2958
- MSC (2010): Primary 35J60
- DOI: https://doi.org/10.1090/proc/12960
- MathSciNet review: 3487227