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.

中文翻译：

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m-超凸域的几何。

我们根据势垒函数，包络线，耗竭函数和Jensen测度研究了Caffarelli–Nirenberg–Spruck模型中m-正则域的几何形状。我们证明，除其他事项外，每个m-超凸域都接受穷举函数，该函数是负的，平滑的，严格的m-次谐波，并且具有m -Hessian测度的界。