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<p>In this note, we revisit recent Liouville-type and rigidity results for the CR Yamabe equation established in [<CitationRef CitationID="CR4">4</CitationRef>, <CitationRef CitationID="CR5">5</CitationRef>]. By refining their arguments, we obtain improved Liouville theorems and rigidity statements on complete noncompact Sasakian manifolds which is stated in dimension 5 in [<CitationRef CitationID="CR5">5</CitationRef>]. Moreover, we provides a short and self-contained proof of a Liouville theorem given in [<CitationRef CitationID="CR4">4</CitationRef>] on the Heisenberg group. Our approach combines integral identities of Jerison–Lee type with suitable energy estimates. A novel thing is that we do not need to use the test function as in [<CitationRef CitationID="CR5">5</CitationRef>].</p>

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On Liouville properties of CR Yamabe equations in Sasakian manifolds

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Le Huy Chuan,
  • Nguyen Thac Dung,
  • Nguyen Van Hoang

摘要

In this note, we revisit recent Liouville-type and rigidity results for the CR Yamabe equation established in [4, 5]. By refining their arguments, we obtain improved Liouville theorems and rigidity statements on complete noncompact Sasakian manifolds which is stated in dimension 5 in [5]. Moreover, we provides a short and self-contained proof of a Liouville theorem given in [4] on the Heisenberg group. Our approach combines integral identities of Jerison–Lee type with suitable energy estimates. A novel thing is that we do not need to use the test function as in [5].