Monge-Amp\`ere equations with right-hand sides of polynomial growth
Analysis of PDEs
2024-06-04 v2 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2404.01040,
title = {Monge-Amp\`ere equations with right-hand sides of polynomial growth},
author = {Beomjun Choi and Kyeongsu Choi and Soojung Kim},
journal= {arXiv preprint arXiv:2404.01040},
year = {2024}
}
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