manuscripta mathematica

, 131:179

On the negativity of higher order derivatives of Dirichlet’s energy in plateau’s problem

Open AccessArticle

DOI: 10.1007/s00229-009-0316-x

Cite this article as:
Tromba, A.J. manuscripta math. (2010) 131: 179. doi:10.1007/s00229-009-0316-x


We calculate higher order derivatives of Dirichlet’s Energy at a branched minimal surface in the direction of Forced Jacobi Fields discovered by the author and R. Böhme. We show that, under certain conditions these derivatives can be made negative, while all lower order derivatives vanish. This is the first time that derivatives of order greater than three have been calculated.

Mathematics Subject Classification (2000)

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© The Author(s) 2009

Authors and Affiliations

  1. 1.University of CaliforniaSanta CruzUSA