Peak Set Crossing all the Circles

Abstract

Let

\Omega\subset\Bbb C^{d}

be a circular, bounded, strictly convex domain with

C^{2}

boundary. We construct a peak set

K\subset\partial\Omega

which intersects all the circles in

\partial\Omega

with the center at zero. In particular Hausdorff dimension of

K

is at least

2d-2

.

Contact details are reproduced from the original publication and may be historical.

Politechnika Krakowska, Instytut Matematyki, ul. Warszawska 24, 31-155 Kraków, Poland

32A05; 32A35

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press LLC.