Stability of Gromov Hyperbolicity Articles uri icon

publication date

  • January 2009

start page

  • 77

end page

  • 96

issue

  • 2

volume

  • 2

international standard serial number (ISSN)

  • 2065-5851

electronic international standard serial number (EISSN)

  • 2065-3506

abstract

  • A main problem when studying any mathematical property is to determine its stability, i.e., under what type of perturbations it is preserved. With this aim, here we study the stability of Gromov hyperbolicity, a property which has been proved to be fruitful in many fields. First of all we analyze the stability under appropriate limits, in the context of general metric spaces. We also prove the stability under some transformations in Riemann surfaces, even though the original surface and the modified one are not quasi-isometric.