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We compute conformal anomalies for conformal field theories with freeconformal scalars and massless spin $1/2$ fields in hyperbolic space$\mathbb{H}^d$ and in the ball $\mathbb{B}^d$, for $2\leq d\leq 7$. Thesespaces are related by a conformal transformation. In even dimensional spaces,the conformal anomalies on $\mathbb{H}^{2n}$ and $\mathbb{B}^{2n}$ are shown tobe identical. In odd dimensional spaces, the conformal anomaly on$\mathbb{B}^{2n+1}$ comes from a boundary contribution, which exactly coincideswith that of $\mathbb{H}^{2n+1}$ provided one identifies the UV short-distancecutoff on $\mathbb{B}^{2n+1}$ with the inverse large distance IR cutoff on$\mathbb{H}^{2n+1}$, just as prescribed by the conformal map. As anapplication, we determine, for the first time, the conformal anomalycoefficients multiplying the Euler characteristic of the boundary for scalarsand half-spin fields with various boundary conditions in $d=5$ and $d=7$.

Boundary Conformal Anomalies on Hyperbolic Spaces and Euclidean Balls