Stable minimal surfaces of finite total curvature (Q1607496)

For complete oriented minimal surfaces of finite total curvature and non-zero genus in Euclidean space the following main theorem is proved: Given any closed Riemannian surface \(\Sigma\) of genus 2 and a Weierstrass point \(p\in\Sigma\), and any \(n\geq 11\), there exists a stable conformal minimal embedding of \(\Sigma\setminus \{p\}\) into \(E^{2n}\) of finite total curvature with respect to \(-2\pi(n+5)\), which is not holomorphic with respect to any complex structure compatible with the Euclidean metric.