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Existence of entire solutions to the Monge-Ampère equation
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 4, August 2014
- pp. 1093-1106
- 10.1353/ajm.2014.0029
- Article
- Additional Information
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We prove the existence of infinitely many entire convex solutions to the Monge-Amp\`ere equation
${\rm det} D^2 u=f$ in ${\Bbb R}^n$, assuming that the inhomogeneous term $f\ge 0$ and is of polynomial growth
at infinity. When $f$ satisfies the doubling condition, we show that solution is of polynomial growth.
As an application, we resolve the existence of translating solutions to a class of Gauss curvature flow.