Minimal Surfaces and Functions of Bounded Variation
Enrico Giusti
Birkhäuser Boston
Contents:

Introduction vii 
Part I: Parametric Minimal Surfaces 
Chapter 1. Functions of Bounded Variation and Caccioppoli Sets . 3 
Chapter 2. Traces of BV Functions 30 
Chapter 3. The Reduced Boundary 42 
Chapter 4. Regularity of the Reduced Boundary 52 
Chapter 5. Some Inequalities 63 
Chapter 6. Approximation of Minimal Sets (I) 74 
Chapter 7. Approximation of Minimal Sets (II) 85 
Chapter 8. Regularity of Minimal Surfaces 97 
Chapter 9. Minimal Cones 104 
Chapter 10. The First and Second Variation of the Area . . . . 115 
Chapter 11. The Dimension of the Singular Set 128 
Part II: Non-Parametric Minimal Surfaces 
Chapter 12. Classical Solutions of the Minimal Surface Equation 137 
Chapter 13. The a priori Estimate of the Gradient 151 
Chapter 14. Direct Methods 160 
Chapter 15. Boundary Regularity 172 
Chapter 16. A Further Extension of the Notion of Non-Parametric 
Minimal Surface 182 
Chapter 17. The Bernstein Problem 201 
Appendix A 218 
Appendix В 224 
Appendix С 226 
Bibliography 235 
Subject Index 239