Domínguez Vázquez, MiguelSanmartín López, Víctor2024-03-052024-03-052024Domínguez-Vázquez M, Sanmartín-López V. Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank. Compositio Mathematica. 2024;160(2):451-462. doi:10.1112/S0010437X230076500010-437Xhttp://hdl.handle.net/10347/33000We construct inhomogeneous isoparametric families of hypersurfaces with non-austere focal set on each symmetric space of non-compact type and rank ≥3. If the rank is ≥4, there are infinitely many such examples. Our construction yields the first examples of isoparametric families on any Riemannian manifold known to have a non-austere focal set. They can be obtained from a new general extension method of submanifolds from Euclidean spaces to symmetric spaces of non-compact type. This method preserves the mean curvature and isoparametricity, among other geometric propertieseng© 2024 The Author(s). This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial licence (https://creativecommons.org/licenses/by-nc/4.0)Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/Isoparametric hypersurfaceInhomogeneousAustere submanifoldSymmetric spaceNon-compact typeHyperpolarExtensionjournal article10.1112/S0010437X230076501570-5846open access