The logarithmic center of a planar region Academic Article uri icon


  • Given a bounded region S S in the complex plane, let f ( ) = S log | z | d f(\beta ) = {smallint _S}log |z - \beta |d area for \beta any complex number. A logarithmic center of S S is an alpha which minimizes f ( ) f(\beta ) . When is alpha unique? Conjecture. If S S is convex then alpha is unique. Theorem. If S S is convex and symmetric about some line, then alpha is unique.

published proceedings

  • Proceedings of the American Mathematical Society

author list (cited authors)

  • Hensley, D.

citation count

  • 0

complete list of authors

  • Hensley, Douglas

publication date

  • January 1976