Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The logarithmic center of a planar region


Author: Douglas Hensley
Journal: Proc. Amer. Math. Soc. 57 (1976), 266-270
MSC: Primary 31A10
DOI: https://doi.org/10.1090/S0002-9939-1976-0407291-8
MathSciNet review: 0407291
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Given a bounded region $ S$ in the complex plane, let $ f(\beta ) = {\smallint _S}\log \vert z - \beta \vert d$ area for $ \beta $ any complex number. A logarithmic center of $ S$ is an $ \alpha $ which minimizes $ f(\beta )$. When is $ \alpha $ unique?

Conjecture. If $ S$ is convex then $ \alpha $ is unique.

Theorem. If $ S$ is convex and symmetric about some line, then $ \alpha $ is unique.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 31A10

Retrieve articles in all journals with MSC: 31A10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0407291-8
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society