The Non-Linear Laplacian for Finsler Manifolds

摘要: For a Finsler manifold (M,F), there is canonical energy function E defined on the Sobolev space. The variation of gives rises to non-linear Laplacian. Although this Laplacian non-linear, it has close relationship with curvatures and other geometric quantities. There are two involved. first one Ricci curvature, which Riemannian quantity, second mean tangent curvature in [S2]. non-Riemannian quantity. In report, we shall briefly describe recent developments study