  Combining the sharp isoperimetric inequality established by Z. Balogh and A.
Krist\'aly [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an
anisotropic symmetrization argument, we establish sharp Morrey-Sobolev
inequalities on $n$-dimensional Finsler manifolds having nonnegative $n$-Ricci
curvature. A byproduct of this method is a Hardy-Sobolev-type inequality in the
same geometric setting. As applications, by using variational arguments, we
guarantee the existence/multiplicity of solutions for certain eigenvalue
problems and elliptic PDEs involving the Finsler-Laplace operator. Our results
are also new in the Riemannian setting.
