### Mathematics Lecture Series

Posted:

**Tue Aug 21, 2012 2:51 pm**Mathematics Lecture Series, Fall 2012

Fresno State

Dr. Bogdan Suceava

California State University, Fullerton

"Geometries Induced by Logarithmic Oscillations and their Natural Extensions"

Friday, August 24, 2012

from 4:00 p.m. to 5:00 p.m.

Science 145

Introduced originally in 1934, Barbilianâ€™s metrization procedure induced a distance on a planar domain by a metric formula given by the so-called logarithmic oscillation. In 1959, Barbilian generalized this process to domains of a more general form, withstanding not necessarily on planar sets, but in a more abstract setting. We will show that there exists more general classes of distances than the ones produced by logarithmic oscillation. As a consequence, we will present the most general form of Barbilianâ€™s metrization procedure. Additionally, in a recent work written with W. G. Boskoff, we are introducing a new distance on a subset of the n-dimensional real space. We will prove it generates an example of Gromov hyperbolic distance on the punctured open unit ball and then study its geometric properties and its relations with other remarkable metrics.

For further information, please contact Dr. Tamas Forgacs at (559) 278-4907 or e-mail tforgacs@csufresno.edu.