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The Geometry of m-Hyperconvex Domains
Per Åhag1, Rafał Czyż2, Lisa Hed1
11Department of Mathematics and Mathematical Statistics, Umeå University, 901 87 Umeå, Sweden.
Abstract:
We study the geometry of m-regular domains within the Caffarelli-Nirenberg-Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every m-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly m-subharmonic, and has bounded m-Hessian measure.
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