manuscripta mathematica

, Volume 131, Issue 1, pp 179-197

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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


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)

49Q05 58E12