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The First Main Theorem; Non-exceptional Branch Points; The Non-vanishing of the Lth Derivative of Dirichlet’s Energy

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

Abstract

Let us state our main goal: Assuming that Open image in new window is a nonplanar minimal surface in normal form having w=0 as a branch point of order n and index m, we want to show that \(\hat{X}\) cannot be a weak relative minimizer of Dirichlet’s integral D in the class Open image in new window . Unfortunately this goal cannot be achieved for all branch points but only for non-exceptional ones and special kinds of exceptional ones. In this chapter we investigate the non-exceptional branch points, while in Chaps. 5 and 6 we deal with the exceptional ones. The main result of the present section – our First Main Theorem – is the following

Keywords

Normal Form Minimal Surface 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.

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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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