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Spectral geometry of \(V\)-manifolds and its application to harmonic maps. (English) Zbl 0806.58005

Greene, Robert (ed.) et al., Differential geometry. Part 1: Partial differential equations on manifolds. Proceedings of a summer research institute, held at the University of California, Los Angeles, CA, USA, July 8-28, 1990. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 1, 93-99 (1993).
The author develops a spectral theory for \(V\)-manifolds (by proving the classical Rellich and Sobolev lemmas) and uses the (extended) heat equation method to derive the theorem of Eells-Sampson to the effect that any map of a compact \(V\)-manifold \(M\) into a compact Riemannian manifold \(N\) with nonpositive sectional curvature is homotopic to a harmonic map.
For the entire collection see [Zbl 0773.00022].
Reviewer: G.Tóth (Camden)

MSC:

58C40 Spectral theory; eigenvalue problems on manifolds
58E20 Harmonic maps, etc.
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