Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity
Analysis of PDEs
2022-02-14 v1
Abstract
In this paper, we establish the asymptotic expansion at infinity of gradient graph in dimension 2 with vanishing mean curvature at infinity. This corresponds to our previous results in higher dimensions and generalizes the results for minimal gradient graph on exterior domain in dimension 2. Different from the strategies for higher dimensions, instead of the equivalence of Green's function on unbounded domains, we apply a version of iteration methods from Bao--Li--Zhang [Calc.Var PDE, 52(2015), pp. 39-63] that is refined by spherical harmonic expansions to provide a more explicit asymptotic behavior than known results.
Keywords
Cite
@article{arxiv.2202.05415,
title = {Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity},
author = {Zixiao Liu and Jiguang Bao},
journal= {arXiv preprint arXiv:2202.05415},
year = {2022}
}