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3 results

  • DEFORMING A CONVEX DOMAIN INTO A DISK BY KLAIN’S CYCLIC REARRANGEMENT

  • Part of
  • YUNLONG YANG, DEYAN ZHANG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 97 / Issue 2 / April 2018
    Published online by Cambridge University Press:
    20 February 2018, pp. 313-319
    Print publication:
    April 2018
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  • For a convex domain, we use Klain’s cyclic rearrangement to obtain a sequence of convex domains with increasing area and the same perimeter which converges to a disk. As a byproduct, we give a proof of the classical isoperimetric inequality in the plane.

  • A NOTE ON RANDOM HOLOMORPHIC ITERATION IN CONVEX DOMAINS

  • Filippo Bracci
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 51 / Issue 2 / June 2008
    Published online by Cambridge University Press:
    28 July 2008, pp. 297-304
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  • We introduce a geometric condition of Bloch type which guarantees that a subset of a bounded convex domain in several complex variables is degenerate with respect to every iterated function system. Furthermore, we discuss the relations of such a Bloch-type condition with the analogous hyperbolic Lipschitz condition.