Relationship between $\gamma_n(A + B)$, $\gamma_k(A)$, and $\gamma_{n-k}(B)$, where $A \subseteq V$, $B \subseteq V^\perp$, and $\gamma_n := N(0,I_n)$

Question

Let $\gamma_n = \gamma_1^{\otimes n}$ be the standard gaussian measure on $\mathbb R^n$ and let $V$ be a $k$-dimensional subspace of $\mathbb R^n$ with orthogonal completment $V^\perp$. Let $A$ and $B$ be Borel measurable subsets of $\mathbb R^n$ such that $A \subseteq V$ and $B \subseteq V^\perp$, and let $C:= A+B$ be the Minkowski sum of $A$ and $B$.

Question. Is there any nontrivial relationship between $\gamma_n(C)$, $\gamma_k(A)$, and $\gamma_{n-k}(B)$ ?