Advertisement

Boundary Branch Points

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

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

Personalised recommendations