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Metrics and convergence in moduli spaces of maps
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 3, pp. 497-526.

Nous présentons un cadre général pour l’étude de la convergence des familles d’applications entre variétés dont les domaines de définition sont distincts. Étant données deux variétés M et N, M étant munie d’une forme volume, nous considérons des familles d’applications dans l’ensemble {(φ,B φ )B φ M,φ:B φ NavecB φ ,φmesurable} et nous définissons une distance sur cet ensemble, de type distance L 1 généralisée. Nous démontrons que l’espace métrique ainsi obtenu est toujours complet. Nous nous concentrons ensuite sur l’étude des propriétés de convergence de telles familles d’applications.

We provide a general framework to study convergence properties of families of maps between manifolds which have distinct domains. For manifolds M and N where M is equipped with a volume form we consider families of maps in the collection {(φ,B φ )B φ M,φ:B φ NwithB φ ,φbothmeasurable} and we define a distance function similar to a generalized L 1 distance on such a collection. We show that the resulting metric space is always complete. We then shift our focus to exploring the convergence properties of families of such maps.

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DOI : https://doi.org/10.5802/afst.1577
@article{AFST_2018_6_27_3_497_0,
     author = {Joseph Palmer},
     title = {Metrics and convergence in moduli spaces of maps},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {497--526},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 27},
     number = {3},
     year = {2018},
     doi = {10.5802/afst.1577},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1577/}
}
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Joseph Palmer. Metrics and convergence in moduli spaces of maps. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 27 (2018) no. 3, pp. 497-526. doi : 10.5802/afst.1577. https://afst.centre-mersenne.org/articles/10.5802/afst.1577/

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