@Article{ATA-37-1,
author = {Gui, Changfeng and Qinfeng, Li},
title = {Completion of $\mathbb{R}^2$ with a Conformal Metric as a Closed Surface},
journal = {Analysis in Theory and Applications},
year = {2021},
volume = {37},
number = {1},
pages = {59--73},
abstract = {<p style="text-align: justify;">In this paper, we obtain some asymptotic behavior results for solutions to the prescribed Gaussian curvature equation. Moreover, we prove that under a conformal metric in $\mathbb{R}^2$, if the total Gaussian curvature is $4\pi$, the conformal area of $\mathbb{R}^2$ is finite and the Gaussian curvature is bounded, then $\mathbb{R}^2$ is a compact $C^{1,\alpha}$ surface after completion at $\infty$, for any $\alpha \in (0,1)$. If the Gaussian curvature has a Hölder decay at infinity, then the completed surface is $C^2$. For radial solutions, the same regularity holds if the Gaussian curvature has a limit at infinity.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2021.pr80.10},
url = {https://global-sci.com/article/73777/completion-of-mathbbr2-with-a-conformal-metric-as-a-closed-surface}
}