Defining functions for unbounded $C^m$ domains
Copyright policy )Defining functions for unbounded $C^m$ domains
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.
- University of Arkansas System United States
- University of Arkansas at Fayetteville United States
Mathematics - Differential Geometry, uniformly \(C^m\) defining function, Mathematics - Complex Variables, defining function, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, Strongly pseudoconvex domains, 53A07, 58C25, 58C07, 32T15, Differential Geometry (math.DG), signed distance function, FOS: Mathematics, Complex Variables (math.CV), unbounded domains, Convexity of real functions of several variables, generalizations
Mathematics - Differential Geometry, uniformly \(C^m\) defining function, Mathematics - Complex Variables, defining function, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, Strongly pseudoconvex domains, 53A07, 58C25, 58C07, 32T15, Differential Geometry (math.DG), signed distance function, FOS: Mathematics, Complex Variables (math.CV), unbounded domains, Convexity of real functions of several variables, generalizations
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