Completion of R2 with a Conformal Metric as a Closed Surface
Year: 2021
Author: Changfeng Gui, Qinfeng Li
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 59–73
Abstract
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 R2, if the total Gaussian curvature is 4π, the conformal area of R2 is finite and the Gaussian curvature is bounded, then R2 is a compact C1,α surface after completion at ∞, for any α∈(0,1). If the Gaussian curvature has a Hölder decay at infinity, then the completed surface is C2. For radial solutions, the same regularity holds if the Gaussian curvature has a limit at infinity.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2021.pr80.10
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 59–73
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Gaussian curvature conformal geometry semilinear equations entire solutions.
Author Details
Changfeng Gui Email
Qinfeng Li Email
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