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...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＋T2The surfaces in the class OHD and the clase of planar surfaces satisfy dimT1 =0. A.Pfluger 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.展开更多
基金A.Fernández is partially supported by the Grant BFM2002-04801J.Pérez by the Grant BFM2002-00141.
文摘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＋T2The surfaces in the class OHD and the clase of planar surfaces satisfy dimT1 =0. A.Pfluger 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.
