Galloway’s compactness theorem on Finsler manifolds

On the conformal group of Finsler manifolds

We generalize to the Finsler case, the Lelong-Ferrand-Obatta Theorem about the compactness of conformal groups of compact Riemannian manifolds, except, the standard sphere.

Relative volume comparison theorems in Finsler geometry and their applications

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

A Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds

In this paper, we prove that the Hodge-Laplace operator on strongly pseudoconvex compact complex Finsler manifolds is a self-adjoint elliptic operator. Then, from the decomposition theorem for self-adjoint elliptic operators, we obtain a Hodge decomposition theorem on strongly pseudoconvex compact complex Finsler manifolds. M.S.C. 2010: 53C56, 32Q99.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...