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Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity

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The second author is supported by National Natural Science Foundation of China 11871102 and 11631002

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  • 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.

    Mathematics Subject Classification: Primary: 35J60, 35C20; Secondary: 35B20.


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