Defining Functions for Unbounded $C^m$ Domains

Details Defining Functions for Unbounded $C^m$ Domains Defining Functions for Unbounded $C^m$ Domains

2011-11-17

arxiv.org/abs/1111.4177v1

Mathematics

Differential Geometry

14 pages

Scientific paper

For a domain $\Omega\subset\mathbb R^n$, we introduce the concept of a
uniformly $C^m$ defining function. We characterize uniformly $C^m$ defining
functions in terms of the signed distance function for the boundary and provide
a large class of examples of unbounded domains with uniformly $C^m$ defining
functions. Some of our results extend results from the bounded case.

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