The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary

• Dongwei Gu ^[1] ; Ngoc Cuong Nguyen ^[2]
  1. [1] Jagiellonian University

     Jagiellonian University

     Kraków, Polonia

     
  2. [2] Pohang University of Science and Technology

     Pohang University of Science and Technology

     Corea del Sur

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 18, Nº 4, 2018, págs. 1189-1248
• Idioma: inglés
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• Resumen

  • We solve the classical Dirichlet problem for a general complex Hessian equation on a small ball in Cn. Then, we show that there is a continuous solution, in pluripotential theory sense, to the Dirichlet problem on compact Hermitian manifolds with boundary that equipped locally conformal Kähler metrics, provided a subsolution.