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In this paper, we provide a fully detailed proof of the well-known fact that the Sobolev norm is independent of the choice of metric when (M, g) is a compact Riemannian manifold. This result is widely used in the theory of Sobolev spaces, but it is typically stated as an elementary fact without a complete proof.

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A Simple Proof of Metric Independence of Sobolev Norms on Compact Manifolds

  • 会议论文

  • 发表日期：

    2026年

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  • Carlos D. Velázquez-Mendoza,
  • María de los Ángeles Sandoval-Romero

摘要

In this paper, we provide a fully detailed proof of the well-known fact that the Sobolev norm is independent of the choice of metric when (M, g) is a compact Riemannian manifold. This result is widely used in the theory of Sobolev spaces, but it is typically stated as an elementary fact without a complete proof.