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arXiv:2404.01040 [math.AP]AbstractReferencesReviewsResources

Monge-Ampère equations with right-hand sides of polynomial growth

Beomjun Choi, Kyeongsu Choi, Soojung Kim

Published 2024-04-01, updated 2024-06-01Version 2

We study the regularity and the growth rates of solutions to two-dimensional Monge-Amp\`ere equations with the right-hand side exhibiting polynomial growth. Utilizing this analysis, we demonstrate that the translators for the flow by sub-affine-critical powers of the Gauss curvature are smooth, strictly convex entire graphs. These graphs exhibit specific growth rates that depend solely on the power of the flow.

Comments: A part of this work was introduced in arXiv:2104.13186v1; however, we have separated and further elaborated the result to accommodate issues that will be dealt in the revision of arXiv:2104.13186. In v2, we generalized the main theorems slightly so that they apply for broader class of equations
Categories: math.AP, math.DG
Subjects: 53E99, 35J96
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