Monge-Amp\`ere equations with right-hand sides of polynomial growth

Autor:	Choi, Beomjun, Choi, Kyeongsu, Kim, Soojung
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry 53E99 35J96
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.01040 Zobrazit plný text záznamu View this record from Arxiv