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)


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


Normal Form Minimal Surface 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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