In this paper,we study the growth of fundamental groups of Finsler manifolds.Some relationships between the growth of fundamental groups and the volume growth of universal covers of Finsler manifolds are found.Some estimates of entropies and the number of generators of fundamental groups of Finsler manifolds are given.Moreover,the quasi-isometry and the geometric norm in Finsler geometry are considered.
The author studies the regularity of energy minimizing maps from Finsler manifolds to Riemannian manifolds. It is also shown that the energy minimizing maps are smooth, when the target manifolds have no focal points.
Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in. These apriori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with nonnegative sectional curvature.
This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generalizes Li＇s results in [2] and [3].
