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Exceptional Branch Points Without the Condition k>l

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

Abstract

Now let Open image in new window be a nonplanar minimal surface in normal form at the exceptional branch point w=0 with \(k \not= l\) which does not satisfy k>l. We have
$$\hat{X}_w (w) = (A_1 w^n + A_2w^{n+1} + \cdots, R_m w^m + \cdots)$$
with m>n, \(A_{1} \not= 0\), \(R_{m} \not= 0\). As in Chap. 5 we introduce C j and \(C'_{j} \in \mathbb{R}^{2}\) by Set
$$\varTheta_j := (j-1) + (n+1);$$
then
$$w \hat{X}_w (w) = \biggl(A_1 w^{n+1} + \sum_{j> 1} C_j w^{\varTheta_j} + \sum _{j> 1} C'_j w^{\varTheta_j}, R_m w^{m+1} + \cdots\biggr).$$

Keywords

Normal Form Holomorphic Function Minimal Surface Differential Geometry Periodic Function 
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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