Shin-ichi OHTA (Kyoto University)
Cheeger-type Sobolev spaces for metric space targets
Abstract.
We generalize the Sobolev space defined by Cheeger for functions to that for maps into an arbitrary metric space. We prove the minimality of the local Lipschitz constant function (Lip u) for a Lipschitz map (u) into an Alexandrov space with an upper curvature bound. By using this, we also show the harmonicity of totally geodesic maps from a Riemannian manifold to an Alexandrov space with nonpositive curvature.

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