Let $M^3$ be a compact and oriented Riemannian manifold. For each $1 \leq k \leq N$, let $\alpha_k$ be the integral current defined by
$$\alpha_k(\omega) = \int_{S_k} \langle \omega(x), \tau_k(x) \rangle \theta_k(x) d \mathcal{H}^2(x), \quad \omega \in \Omega^2(M)$$
where $S_k$ is a compact, connected and oriented embedded surface, $\tau_k$ is a $2$-field that orients $S_k$ and $\theta_k$ is an integrable positive integer-valued function on $S_k$ (the multiplicity of $S_k$). The mass of each $\alpha_k$ is given by
$$\mathbb{M}(\alpha_k) := \sup \{ \alpha_k(\omega) : \omega \in \Omega^2(M), \Vert \omega \Vert \leq 1 \}.$$
Suppose that the collection $\{ S_1, \dots, S_N \}$ is disjoint in $M$. Let
$$\alpha = \sum_{k=1}^N \alpha_k$$
and
$$\alpha' = \sum_{k=1}^{N-1} \alpha_k = \alpha - \alpha_{N}.$$
My question is: does it hold that the mass of $\alpha'$ is smaller than the mass of $\alpha$?