Repositorio de producción científica de la Universidad de Sevilla

Continuous selections of Lipschitz extensions in metric spaces

Opened Access Continuous selections of Lipschitz extensions in metric spaces

Citas

buscar en

Estadísticas
Icon
Exportar a
Autor: Espínola García, Rafael
Nicolae, Adriana
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2015-09
Publicado en: Revista Matemática Complutense, 28 (3), 741-759.
Tipo de documento: Artículo
Resumen: 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.
Cita: Espínola García, R. y Nicolae, A. (2015). Continuous selections of Lipschitz extensions in metric spaces. Revista Matemática Complutense, 28 (3), 741-759.
Tamaño: 221.9Kb
Formato: PDF

URI: http://hdl.handle.net/11441/44795

DOI: 10.1007/s13163-015-0171-0

Ver versión del editor

Mostrar el registro completo del ítem


Esta obra está bajo una Licencia Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internacional

Este registro aparece en las siguientes colecciones