2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72903The Teichmuller space Teich(S) of a surface S in genus g>1 is a real submanifold of the quasifuchsian space QF(S). We show that the determinant of the Laplacian det'(Delta) on Teich(S) has a unique holomorphic extension to QF(S).11 pages, LaTeX; added an important remark in Introduction and added the corresponding reference, typos correctedComplex VariablesDifferential Geometry32G15; 58J52text