Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity
Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity
复制标题
DOI：
--
复制
发表时间：
2022-02
期刊：
影响因子：
--
通讯作者：
Zixiao Liu;J. Bao
中科院分区：
文献类型：
--
作者：
Zixiao Liu;J. Bao
本文建立了平均曲率在无穷远处消失的2维梯度图在无穷远处的渐近展开式。这与我们之前在高维上的结果相对应，并推广了在2维外域上最小梯度图的结果。与高维的策略不同，我们采用的不是无界域上格林函数的等价性，而是张宝丽[Calc.Var PDE, 52(2015), pp. 39-63]的迭代方法版本，该迭代方法通过球面调和展开进行了改进，以提供比已知结果更明确的渐近行为。
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.