A volume comparison theorem for Finsler manifolds

Galloway’s compactness theorem on Finsler manifolds

The compactness theorem of Galloway is a stronger version of the Bonnet-Myers theorem allowing the Ricci scalar to take also negative values from a set of real numbers which is bounded below. In this paper we allow any negative value for the Ricci scalar, and adding a condition on its average, we find again that the manifold is compact and provide an upper bound of its diameter. Also, with no c...

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...

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.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Homotheties of Finsler Manifolds *

We give a new and complete proof of the following theorem, discovered by Detlef Laugwitz: (forward) complete and connected finite dimensional Finsler manifolds admitting a proper homothety are Minkowski vector spaces. More precisely, we show that under these hypotheses the Finsler manifold is isometric to the tangent Minkowski vector space of the fixed point of the homothety via the exponential...