Harmonic measures realized as Hausdorff measures

Let M be a compact negatively curved Riemannian manifold with universal covering M and let #delta#_0 > 0 be the negative of the bottom of the positive spectrum of the Laplacean #DELTA# on M. We use methods from ergodic theory to show that #DELTA# + #delta#_0 admits a Green's function which decays exponentially with the distance. Moreover for almost every point #zeta# element of #partial deriv#M with respect to a suitable Borel-measure which is positive on open sets the unique minimal positive #DELTA# + #partial deriv#_0 -#epsilon#-harmonic functions on M with pole at #zeta# normalized at a point x element of M converge as #epsilon# #-># 0 uniformly on compact sets to a minimal positive #DELTA# + #delta#_0-harmonic function. (orig.)Available from TIB Hannover: RO 5389(406) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman