Removable sets for Hölder continuous solutions of A-harmonic functions on Finsler manifolds

Abstract We show that a closed set S S is removable for α -Hölder continuous A A -harmonic functions in a domain Ω within a reversible Finsler manifold (M, F, V) (M, F, V) of dimension n 2 n ≥ 2. This removability holds under certain assumptions on (M, F, V) (M, F, V) and the variable exponent p, provided that for every compact subset K S K ⊂ S, the Hausdorff measure of K with dimension n₁ - pK^+ + (pK^+ - 1) n 1 - p K + + α (p K + - 1) is zero. Here, pK^+ = K p p K + = sup K p, and n₁ n 1 is a dimension exponent satisfying the growth condition V (B (x, r) ) Kr^ {n₁} V (B (x, r) ) ≤ K r n 1 for all balls. The second main result establishes an estimate for (B (x, r) ): = \{ ₁ (ₗ, ₑ)