Uniqueness results on CR manifolds

• Pak Tung Ho ^[1]
  1. [1] Sogang University

     Sogang University

     Corea del Sur

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 2, 2021, págs. 853-870
• Idioma: inglés
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• Resumen

  • In this paper we show the uniqueness of the constant solution to a general Yamabe-type equation on a compact pseudohermitian manifold. The Riemannian version was first proved by Bidaut-V ́eron and V ́eron. In another direction, we make use of the vanishing property of two eigenfunctions of the sub-Laplacian to conclude the nonvanishing of the first cohomology group of a compact pseudohermitian manifold. The corresponding version for the Rieman- nian case was first proved by Gichev.