Prescribing Q-curvature on even-dimensional manifolds with conical singularities

• Aleks Jevnikar ^[1] ; Yannick Sire ^[2] ; Wen Yang ^[3]
  1. [1] Università di Udine

     Università di Udine

     Udine, Italia

     
  2. [2] Johns Hopkins University

     Johns Hopkins University

     Estados Unidos

     
  3. [3] University of Macau, Macau, P. R. China

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 41, Nº 1, 2025, págs. 1-28
• Idioma: inglés
• DOI: 10.4171/RMI/1543
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• Resumen

  • On a 2m-dimensional closed manifold, we investigate the existence of prescribed Q-curvature metrics with conical singularities. We present here a general existence and multiplicity result in the supercritical regime. To this end, we first carry out a blow-up analysis of a 2mth-order PDE associated to the problem, and then apply a variational argument of min-max type. For m>1, this seems to be the first existence result for supercritical conic manifolds different from the sphere.