Journal
GEOMETRIAE DEDICATA
Volume 125, Issue 1, Pages 225-250Publisher
SPRINGER
DOI: 10.1007/s10711-007-9159-3
Keywords
CAT(0)-space; CAT(1)-space; Banach space; Cheeger-type Sobolev space; Dirichlet problem
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We introduce two kinds of the notion of convexity of a metric space, called k-convexity and L-convexity, as generalizations of the CAT(0)-property and of the nonpositively curved property in the sense of Busemann, respectively. 2-uniformly convex Banach spaces as well as CAT(1)-spaces with small diameters satisfy both these convexities. Among several geometric and analytic results, we prove the solvability of the Dirichlet problem for maps into a wide class of metric spaces.
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