Sharp Morrey-Sobolev inequalities and eigenvalue problems on Riemannian- Finsler manifolds with nonnegative Ricci curvature

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 variational arguments, guarantee existence/multiplicity solutions for certain eigenvalue problems elliptic PDEs involving Finsler–Laplace operator. Our results are also new Riemannian