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arXiv · 2403.06782

Mass from an Extrinsic Point of View

Alexandre de Sousa·Frederico Girão
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Abstract

We express the $q$-th Gauss-Bonnet-Chern mass of an immersed submanifold of Euclidean space as a linear combination of two terms: the total $(2q)$-th mean curvature and the integral, over the entire manifold, of the inner product between the $(2q+1)$-th mean curvature vector and the position vector of the immersion. As a consequence, we obtain, for each $q$, a geometric inequality that holds whenever the positive mass theorem (for the $q$-th Gauss-Bonnet-Chern mass) holds.

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Alexandre de Sousa, Frederico Girão. 2024-03-11. Mass from an Extrinsic Point of View. https://doi.org/10.3842/sigma.2025.018

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