A Theory of Branched Minimal Surfaces

1. Introduction
Anthony Tromba

2. Higher Order Derivatives of Dirichlet’s Energy
Anthony Tromba

3. Very Special Case; The Theorem for n+1 Even and m+1 Odd
Anthony Tromba

4. The First Main Theorem; Non-exceptional Branch Points; The Non-vanishing of the L
th Derivative of Dirichlet’s Energy
Anthony Tromba

5. The Second Main Theorem: Exceptional Branch Points; The Condition k>l

Anthony Tromba

6. Exceptional Branch Points Without the Condition k>l

Anthony Tromba

7. New Brief Proofs of the Gulliver–Osserman–Royden Theorem
Anthony Tromba

8. Boundary Branch Points
Anthony Tromba

9. Scholia
Anthony Tromba

Keywords: Mathematics, Functions of a Complex Variable, Sequences, Series, Summability, Differential Geometry, Global Analysis and Analysis on Manifolds