Contents / p2
Introduction / p1
Chapter 1. Triangulation / p6
　§1.1. Collection Φ of local parameters / p6
　§1.2. Triangulation K associated to Φ / p7
　§1.3. Normal subdivision of triangulation K / p10
　§1.4. Naturalized triangulation / p11
　§1.5. Parametrization of lunar domains / p13
　§1.6. Area of lune / p14
Chapter 2. Spaces of differentials / p16
　§2.1. Subspace Λ of Γc / p16
　§2.2. Space Λ' / p17
　§2.3. Finite element interpolations / p19
　§2.4. Harmonic differentials on a lune / p19
　§2.5. Difference of norms of σh and σ'h / p20
Chapter 3. Finite element approximations / p24
　§3.1. Formulation of problems / p24
　§3.2. Finite element approximation ψh in Λ / p26
　§3.3. Finite element approximation ω'h in Λ' / p28
　§3.4. Lemma of Bramble and Zlámal / p29
　§3.5. Pointwise estimate / p29
　§3.6. Smoothness of ω on Ω / p31
　§3.7. Approximation by ψh / p33
　§3.8. Approximation by ω'h / p36
　§3.9. Estimate of ||ω'h - ω̂'|| / p39
Chapter 4. Determination of the periodicity moduli of Riemann surfaces / p41
　§4.1. Periodicity moduli of Riemann surfaces / p41
　§4.2. Calculation of periodicity moduli / p42
　§4.3. Numerical example 1(the case of a ciosed Riemann sueface) / p43
　§4.4. Numerical example 2(the case of acompact bordered Rimann surface) / p51
Chapter 5. Determination of the modulus of quadrilaterals / p60
　§5.1. Quadrilateral on a Riemann surface / p60
　§5.2. Formulation of problems / p60
　§5.3. Numerical example 3(the case of Gaier's example) / p62
　§5.4. Numerical example 4(the case of a riemann surface) / p68
　§5.5. Numerical example 5(the case of an unbounded domain) / p75
　§5.6. Numerical example 6(the case of a curvilinear domain) / p77
References / p81