Minimal Submanifolds
نویسندگان
چکیده
Contents 1. Introduction 2 Part 1. Classical and almost classical results 2 1.1. The Gauss map 3 1.2. Minimal graphs 3 1.3. The maximum principle 5 2. Monotonicity and the mean value inequality 6 3. Rado's theorem 8 4. The theorems of Bernstein and Bers 9 5. Simons inequality 10 6. Heinz's curvature estimate for graphs 10 7. Embedded minimal disks with area bounds 11 8. Stable minimal surfaces 11 9. Regularity theory 12 9.1. ǫ–regularity and the singular set 13 9.2. Tangent cone analysis 13 Part 2. Embedded minimal surfaces 14 10.1. Multi–valued graphs 14 10.2. The sublinear growth of the separation 15 11. Embedded minimal surfaces with fixed genus 16 11.
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