Embedded minimal surfaces with three ends associated with the Hoffman-Osserman catenoids

For every positive integer $g$ and every Hoffman-Osserman catenoid in $\mathbb{R}^5$, we construct a complete embedded minimal surface of genus $g$ that is not contained in any proper affine subspace of $\mathbb{R}^5$. These surfaces can be viewed as higher-codimensional analogues of the Costa-Hoffman-Meeks surfaces, associated with the union of the corresponding Hoffman-Osserman catenoid and the plane containing its waist circle. We provide explicit Weierstrass data for these surfaces. Our construction can also be interpreted as restoring conformality to a deformed Costa-Hoffman-Meeks immersion by introducing two additional harmonic coordinate functions.