FINSLER LAPLACIANS AND MINIMAL-ENERGY MAPS
2000 ◽
Vol 11
(01)
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pp. 1-13
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Keyword(s):
The Mean
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For any Finsler manifold, there is a geometrically natural Laplacian operator, called the mean-value Laplacian, which generalizes the Riemannian Laplacian. We show that, like the Riemannian Laplacian (for functions), we can see the vanishing of the mean-value Laplacian at some function f as the minimizing of an energy functional e(f) by f. This energy functional e depends on a Riemannian metric canonically associated to the Finsler metric and on a canonically associated volume form. We relate this construction to a more general construction of Jost, and define a notion of harmonic mappings between Finsler manifolds.