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Christian RemlingChristian Remling is right; in Chapter 6, section 2.4 of Schoen and Yau's Lectures of Differential Geometry, which covers the material presented in your linked paper, we see that the authors define Hausdorff measure and Newton capacity relative to the the ambient embedding into $\mathbb{R}^{n+1}$.

Christian Remling is right; in Chapter 6, section 2.4 of Schoen and Yau's Lectures of Differential Geometry, which covers the material presented in your linked paper, we see that the authors define Hausdorff measure and Newton capacity relative to the the ambient embedding into $\mathbb{R}^{n+1}$.

Christian Remling is right; in Chapter 6, section 2.4 of Schoen and Yau's Lectures of Differential Geometry, which covers the material presented in your linked paper, we see that the authors define Hausdorff measure and Newton capacity relative to the the ambient embedding into $\mathbb{R}^{n+1}$.

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Willie Wong
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Christian Remling is right; in Chapter 6, section 2.4 of Schoen and Yau's Lectures of Differential Geometry, which covers the material presented in your linked paper, we see that the authors define Hausdorff measure and Newton capacity relative to the the ambient embedding into $\mathbb{R}^{n+1}$.