Article
Continuous selections of Lipschitz extensions in metric spaces
Author/s | Espínola García, Rafael
Nicolae, Adriana |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2015-09 |
Deposit Date | 2016-09-07 |
Published in |
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Abstract | This paper deals with the study of parameter dependence of extensions of Lipschitz mappings from the point of view of continuity. We show that if assuming appropriate curvature bounds for the spaces, the multivalued extension ... This paper deals with the study of parameter dependence of extensions of Lipschitz mappings from the point of view of continuity. We show that if assuming appropriate curvature bounds for the spaces, the multivalued extension operators that assign to every nonexpansive (resp. Lipschitz) mapping all its nonexpansive extensions (resp. Lipschitz extensions with the same Lipschitz constant) are lower semi-continuous and admit continuous selections. Moreover, we prove that Lipschitz mappings can be extended continuously even when imposing the condition that the image of the extension belongs to the closure of the convex hull of the image of the original mapping. When the target space is hyperconvex one can obtain in fact nonexpansivity. |
Project ID. | MTM2012-34847C02-01
FQM-127 PN-II-RU-PD-2012-3-0152 |
Citation | Espínola García, R. y Nicolae, A. (2015). Continuous selections of Lipschitz extensions in metric spaces. Revista Matemática Complutense, 28 (3), 741-759. |
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