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math.CA2026
On Almgren's Multiple-valued Functions of Class 1
Nicolau S. Aiex
We prove that all reasonable definitions of multiple-valued functions with continuous derivatives are equivalent, which eliminates inconsistencies in the literature. As an intermed…
math.DG2026
Quantitative Estimates on the Topology and Singular Set of Prescribed Mean Curvature Hypersurfaces
Nicolau S. Aiex, Sean McCurdy, Paul Minter
We establish quantitative topological and singularity properties for (certain) prescribed mean curvature (PMC) hypersurfaces in Riemannian manifolds . Indeed, if…