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<p>We prove a Liouville-type theorem for subharmonic functions by assuming a finite weighted Dirichlet integral condition, and then apply it to study the rigidity of complete, non-compact <i>m</i>-quasi-Einstein manifolds. Further, we obtain the triviality of a complete, non-compact <i>m</i>-quasi-Einstein manifold <i>M</i> by imposing certain regularity conditions on the potential function and Ricci curvature constraints on <i>M</i>.</p>

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A Liouville-type theorem for subharmonic functions and its applications to quasi-Einstein manifolds

  • 期刊论文

  • 发表日期：

    2026年3月25日

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  • Rahul Poddar

摘要

We prove a Liouville-type theorem for subharmonic functions by assuming a finite weighted Dirichlet integral condition, and then apply it to study the rigidity of complete, non-compact m-quasi-Einstein manifolds. Further, we obtain the triviality of a complete, non-compact m-quasi-Einstein manifold M by imposing certain regularity conditions on the potential function and Ricci curvature constraints on M.