ON A CLASS OF RIEMANN SURFACES

作     者：Arturo Fernández Javier Pérez 

作者机构：Ciudad UniversitariaSpain 

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

年 卷 期：2006年第22卷第4期

页      面：377-386页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：A.Fernández is partially supported by the Grant BFM2002-04801 J.Pérez by the Grant BFM2002-00141 

主　　题：Harmonic form orthogonal decomposition Diriehlet norm 

摘      要：It is considered the class of Riemann surfaces with dimT1=0, where T1 is a subclass of exactharmonic forms which is one of the factors in the orthogonal decomposition of the space Ω^H of harmonic forms of the surface, namely Ω^H=＊Ω^H＋T1＋＊T0^H＋T0^H＋T2 The surfaces in the class OHD and the clase of planar surfaces satisfy dimT1 =0. *** posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimTl = 0 among the surfaces of the form Sg／K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.