Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 16 (2009), No. 2, 515--521Copyright Heldermann Verlag 2009 Peak Set Crossing all the Circles Piotr Kot Politechnika Krakowska, Instytut Matematyki, ul. Warszawska 24, 31-155 Kraków, Poland pkot@pk.edu.pl [Abstract-pdf] 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 $2d-2$. Keywords: Homogeneous polynomials, peak set, maximum modulus set, inner function. MSC: 32A05; 32A35 [ Fulltext-pdf  (110  KB)] for subscribers only.