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PRESCRIBING GAUSSIAN CURVATURE ON CLOSED RIEMANN SURFACE WITH CONICAL SINGULARITY IN THE NEGATIVE CASE
文献类型：期刊
通讯作者：Yang, YY (reprint author), Renmin Univ China, Dept Math, Beijing 100872, Peoples R China.
期刊名称：ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA影响因子和分区
年：2019
卷：44
页码：167-181
ISSN：1239-629X
关键词：Prescribing Gaussian curvature; conical singularity
所属部门：信息学院
摘要：The problem of prescribing Gaussian curvature on Riemann surface with conical singularities is considered. Let (Sigma, beta) be a closed Riemann surface with a divisor beta, and K-lambda = K+lambda, where K: Sigma -> R is a Holder continuous function satisfying max(Sigma) K = 0, K not equivalent to 0, and lambda is an element of R. If the Euler characteristic chi(Sigma, beta) is negative, then by a variational method, it is proved that there exists a constant lambda* > 0 such that for any lambda ...More
The problem of prescribing Gaussian curvature on Riemann surface with conical singularities is considered. Let (Sigma, beta) be a closed Riemann surface with a divisor beta, and K-lambda = K+lambda, where K: Sigma -> R is a Holder continuous function satisfying max(Sigma) K = 0, K not equivalent to 0, and lambda is an element of R. If the Euler characteristic chi(Sigma, beta) is negative, then by a variational method, it is proved that there exists a constant lambda* > 0 such that for any lambda <= 0, there is a unique conformal metric with the Gaussian curvature K-lambda; for any lambda, 0 < lambda < lambda*, there are at least two conformal metrics having K-lambda its Gaussian curvature; for lambda = lambda*, there is at least one conformal metric with the Gaussian curvature K-lambda*; for any lambda > lambda*, there is no certain conformal metric having K-lambda its Gaussian curvature. This result is an analog of that of Ding and Liu [16], partly resembles that of Borer, Galimberti and Struwe [5], and generalizes that of Troyanov [28] in the negative case. ...Hide

DOI：10.5186/aasfm.2019.4411
百度学术：PRESCRIBING GAUSSIAN CURVATURE ON CLOSED RIEMANN SURFACE WITH CONICAL SINGULARITY IN THE NEGATIVE CASE
语言：外文
被引频次：1
人气指数：2
浏览次数：2
基金：National Science Foundation of ChinaNational Natural Science Foundation of China [11171347, 11471014, 11401575]
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Existence of extremals for critical Trudinger-Moser inequalities via the method of energy estimate.Yang, Yunyan,.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 2019, 479(1), 1281-1291.
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