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On carleman's differential inequality and the equation for gaussian curvature*

 

作者: Gregory S. Rhoads,  

 

期刊: Complex Variables, Theory and Application: An International Journal  （Taylor Available online 1998）
卷期: Volume 36, issue 4  

页码: 393-403

 

ISSN:0278-1077

 

年代: 1998

 

DOI:10.1080/17476939808815120

 

出版商: Gordon and Breach Science Publishers

 

关键词: Conformal metric;differential inequality;subharmonic function;1991 Mathematics Subject Classification Primary 30F45;Primary 30F45;35J60;Secondary 53C21;31A05

 

数据来源: Taylor

 

摘要:

The equation for Gaussian curvature of a conformal metric is a special case of the classical differential equation. δu=f(u) for u ∈C2(ω), where ω⊂R2. We will use a technique introduced by Carleman to find restrictions onfand the set where a subharmonic functionucan satisfy the above equation. This result will generate a relationship between the curvature and the metric of a nonpositively curved surface.

 

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