A Theory of Branched Minimal Surfaces pp 117-168 | Cite as

# Boundary Branch Points

Chapter

## Abstract

In this chapter we first show that Dirichlet’s integral possesses intrinsic second and third derivatives at a minimal surface \(\hat{X}\) on the tangent space *T* _{ X } *M* of *M*:=*H* ^{2}(*∂B*,ℝ^{ n }) of \(X =\hat{X}|_{\partial B}\) on the space \(J(\hat{X})\) of forced Jacobi fields for \(\hat{X}\). In particular it will be seen that \(J(\hat{X})\) is a subspace of the kernel of the Hessian *D* ^{2} *E*(*X*) of Dirichlet’s integral *E*(*X*) defined in (8.1) below, and an interesting formula (see (8.16)) for the second variation of Dirichlet’s integral is derived.

## Keywords

Minimal Surface Tangent Space Branch Point Meromorphic Function Complex Component
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## Copyright information

© Springer-Verlag Berlin Heidelberg 2012