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.
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Phillip Harrington, Andrew Raich, Defining functions for unbounded domains. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1405–1420DOI 10.4171/RMI/762