Mean field equations and domains of first kind

• Daniele Bartolucci ^[1] ; Andrea Malchiodi ^[2]
  1. [1] University of Rome
  2. [2] Scuola Normale Superiore, Pisa
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 4, 2022, págs. 1067-1086
• Idioma: inglés
• DOI: 10.4171/RMI/1351
• Enlaces
  • Texto Completo Ejemplar
• Resumen

  • In this paper, we are interested in understanding the structure of domains of first and second kind, a concept motivated by problems in statistical mechanics and mean field equations. We prove some openness property for domains of first kind with respect to a suitable topology, as well as some sufficient condition, in terms of the Fourier coefficients of the Riemann map, for a simply connected domain to be of first kind. Finally, we show that the set of simply connected domains of first kind is contractible.