Contents vii
§13.5. The Maximum Principle 170
§13.6. Removable Singularities 171
§13.7. Power Series 172
§13.8. Taylor Series 174
Chapter 14. Disk and Plane Rigidity 177
§14.1. Disk Rigidity 177
§14.2. Liouville’s Theorem 179
§14.3. Stereographic Projection Revisited 181
Chapter 15. The Schwarz–Christoffel Transformation 183
§15.1. The Basic Construction 184
§15.2. The Inverse Function Theorem 185
§15.3. Proof of Theorem 15.1 186
§15.4. The Range of Possibilities 188
§15.5. Invariance of Domain 189
§15.6. The Existence Proof 190
Chapter 16. Riemann Surfaces and Uniformization 195
§16.1. Riemann Surfaces 195
§16.2. Maps Between Riemann Surfaces 197
§16.3. The Riemann Mapping Theorem 199
§16.4. The Uniformization Theorem 201
§16.5. The Small Picard Theorem 202
§16.6. Implications for Compact Surfaces 203
Part 4. Flat Cone Surfaces
Chapter 17. Flat Cone Surfaces 207
§17.1. Sectors and Euclidean Cones 207
§17.2. Euclidean Cone Surfaces 208
§17.3. The Gauss–Bonnet Theorem 209
§17.4. Translation Surfaces 211
§17.5. Billiards and Translation Surfaces 213
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