Defining functions for unbounded domains

  • Phillip Harrington

    University of Arkansas, Fayetteville, USA
  • Andrew Raich

    University of Arkansas, Fayetteville, USA


For a domain , we introduce the concept of a uniformly defining function. We characterize uniformly defining functions in terms of the signed distance function for the boundary and provide a large class of examples of unbounded domains with uniformly defining functions. Some of our results extend results from the bounded case.

Cite this article

Phillip Harrington, Andrew Raich, Defining functions for unbounded domains. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1405–1420

DOI 10.4171/RMI/762