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Improved Fractional Sobolev Embeddings on Closed Riemannian Manifolds under Isometric Group Actions

Analysis of PDEs 2026-03-31 v1 Functional Analysis

Abstract

In this paper, we study symmetry-improved fractional Sobolev embeddings on closed Riemannian manifolds under the action of compact isometry groups. We prove that GG-invariant fractional Sobolev spaces embed into higher LpL^p spaces, with corresponding compactness results depending on the minimal orbit dimension. We also investigate the associated optimal constants in the improved critical inequality and in the standard critical inequality under finite-orbit symmetry.

Keywords

Cite

@article{arxiv.2603.28451,
  title  = {Improved Fractional Sobolev Embeddings on Closed Riemannian Manifolds under Isometric Group Actions},
  author = {Hao Tan and Zhipeng Yang},
  journal= {arXiv preprint arXiv:2603.28451},
  year   = {2026}
}

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