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<p>In this work we obtain some uniqueness, nonexistence and rigidity results for complete submanifolds immersed in Riemannian manifolds which guarantee that, under appropriate hypothesis, the only possible such submanifolds are the ones contained in slices. In order to obtain these results we study the height function associated to the submanifold using a powerfull maximum principle for the infinity-Laplacian operator.</p>

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Rigidity Results of Complete Submanifolds in Riemannian Warped Product Via Infinity-Laplacian Operator

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Guilherme F. do Nascimento,
  • Eraldo A. Lima Jr

摘要

In this work we obtain some uniqueness, nonexistence and rigidity results for complete submanifolds immersed in Riemannian manifolds which guarantee that, under appropriate hypothesis, the only possible such submanifolds are the ones contained in slices. In order to obtain these results we study the height function associated to the submanifold using a powerfull maximum principle for the infinity-Laplacian operator.