Abstract
For a Finsler manifold (M,F), there is a canonical energy function E defined on the Sobolev space. The variation of E gives rises to a non-linear Laplacian. Although this Laplacian is non-linear, it has a close relationship with curvatures and other geometric quantities. There are two curvatures involved. The first one is the Ricci curvature, which is a Riemannian quantity, and the second one is the mean tangent curvature defined in [S2]. The mean tangent curvature is a non-Riemannian quantity. In this report, we shall briefly describe the recent developments in the study of this non-linear Laplacian.
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Shen, Z. (1998). The Non-Linear Laplacian for Finsler Manifolds. In: Antonelli, P.L., Lackey, B.C. (eds) The Theory of Finslerian Laplacians and Applications. Mathematics and Its Applications, vol 459. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5282-2_12
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DOI: https://doi.org/10.1007/978-94-011-5282-2_12
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