On the length of lemniscates

Details On the length of lemniscates On the length of lemniscates

2008-05-15

arxiv.org/abs/0805.2295v1

Michigan Math. J., 46 (1999), 409-415

Mathematics

Complex Variables

Scientific paper

We show that for a monic polynomial p of degree d, the length of the level
set {z: |p(z)|=1} is at most 9.2 d, which improves an earlier estimate due to
P. Borwein. For d=2 we show that the extremal level set is the Bernoullis'
Lemniscate. One ingredient of our proofs is the fact that for an extremal
polynomial this level set is connected.

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