论文标题
二维梯度图的渐近扩张，无限级平均曲率消失
Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity
论文作者
论文摘要
在本文中，我们在梯度图2的无穷大范围内建立了渐近膨胀，在无穷大处，平均曲率消失了。这与我们先前在较高维度中的结果相对应，并概括了在维度2中的外部领域上最小梯度图的结果。与较高维度的策略不同，而不是Green在未绑定的域上的功能等效，我们应用了Bao-li-Zhang [calc.var pde，52 norminisy in Collimentials to in bocled域上的功能，而不是bao-li-li and。扩展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.
