In this paper, we introduce isoparametric functions and hypersurfaces in conic Finsler spaces. We find that there are probably other Minkowski spaces besides the hyperplanes, hyperspheres cylinders, such as helicoids. Moreover, give a complete classification of Kropina with constant flag curvature.

In the present paper we deal with a quasilinear elliptic equation involvinga critical Sobolev exponent on non-compact Finsler manifolds, i.e. Randers spaces. Under very general assumptions perturbation prove existence of non-trivial solution. The approach is based direct methods calculus variations. One key step to that energy functional associated problem weakly lower semicontinuous small ball...

Combining the sharp isoperimetric inequality established by Z. Balogh and A. Kristály [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argument, we establish Morrey–Sobolev inequalities on n-dimensional Finsler manifolds having nonnegative n-Ricci curvature. A byproduct of this method is a Hardy–Sobolev-type same geometric setting. As applications, using...

The starting point of the famous structure theorems on Berwald spaces due to Z.I. Szabó [4] is an observation on the Riemann-metrizability of positive definite Berwald manifolds. It states that there always exists a Riemannian metric on the underlying manifold such that its Levi-Civita connection is just the canonical connection of the Berwald manifold. In this paper we present a new elementary...