Completion of R^(2)with a Conformal Metric as a Closed Surface

作     者：Changfeng Gui Qinfeng Li Changfeng Gui;Qinfeng Li

作者机构：Department of MathematicsThe University of Texas at San AntonioSan AntonioTexas 78249USA School of MathematicsHunan UniversityChangshaHunan 410082China 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2021年第37卷第1期

页      面：59-73页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：This research is partially supported by NSF grant DMS-1601885 and DMS-1901914. Theauthors would like to thank Dong Ye for the remark regarding the negative answer ofQuestion 1.2. 

主　　题：Gaussian curvature conformal geometry semilinear equations entire solutions 

摘      要：In this paper,we obtain some asy mptotic behav ior results for solutions to the prescribed Gaussian curvature equation.Moreover,we prove that under a con-formal metric in R^(2),if the total Gaussian curvature is 4π,the conformal area of R^(2)is finite and the Gaussian curvature is bounded,then R^(2)is a compact C^(l,α)surface after completion at∞,for anya∈(0,1).If the Gaussian curvature has a Holder decay at in-finity,then the completed surface is C^(2).For radial solutions,the same regularity holds if the Gaussian curvature has a limit at infinity.