Boundary Branch Points

  • Anthony Tromba
Part of the Springer Monographs in Mathematics book series (SMM)


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.


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

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at Santa CruzSanta CruzUSA

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