Book:Hermann Weyl/The Concept of a Riemann Surface

Subject Matter

 * Analysis

Contents

 * Preface


 * I. Concept and Topology of Riemann Surfaces


 * $\S 1$. Weierstrass' concept of an analytic function
 * $\S 2$. The concept of an analytic form
 * $\S 3$. The relation between the concepts "analytic function" and "analytic form"
 * $\S 4$. The concept of a two-dimensional manifold
 * $\S 5$. Examples of surfaces
 * $\S 6$. Specialization; in particular, differentiable and Riemann surfaces
 * $\S 7$. Orientation
 * $\S 8$. Covering surfaces
 * $\S 9$. Differentials and line integrals. Homology
 * $\S 10$. Densities and surface integrals. The residue theorem
 * $\S 11$. The intersection number


 * II. Functions on Riemann Surfaces


 * $\S 12$. The Dirichlet integral and harmonic differentials
 * $\S 13$. Scheme for the construction of the potential arising from a doublet source
 * $\S 14$. The proof
 * $\S 15$. The elementary differentials
 * $\S 16$. The symmetry laws
 * $\S 17$. The uniform functions on $\mathfrak F$ as a subspace of the additive and multiplicative functions on $\hat {\mathfrak F}$. The Riemann-Roch theorem
 * $\S 18$. Abel's theorem. The inversion problem
 * $\S 19$. The algebraic function field
 * $\S 20$. Uniformization
 * $\S 21$. Riemann surfaces and non-Euclidean groups of motions. Fundamental regions. Poincaré $\Theta$-series
 * $\S 22$. The conformal mapping of a Riemann surface onto itself


 * Index