5 papers
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…
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…
A Curvature Varifold Whose Weak Second Fundamental Form is Not Preserved Under Decompositions
Nicolau S. Aiex
We construct a curvature varifold that does not admit a decomposition whose components are curvature varifolds.
Compactness of the Space of Free Boundary CMC Surfaces with Bounded Topology
Nicolau S. Aiex, Han Hong
We prove that the space of free boundary CMC surfaces of bounded topology, bounded area and bounded boundary length is compact in the graphical sense away from a finite set o…
A Corrected Proof of the Graphical Representation of a Class of Curvature Varifolds by Multiple Valued Functions
Nicolau S. Aiex
We provide a counter-example to Hutchinson's original proof of representation of curvature -varifolds with -integrable second fundamental form and in [6].…