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papers

Publications (18)

math.DG2022

The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density 5/2

Paul Minter

We prove a multi-valued $C^{1, α}$ regularity theorem for the varifolds in the class $S_{2}$ (i.e., stable codimension one stationary integral $n$ -varifolds admitting no tri…

math.AP2024

Fine Structure of Singularities in Area-Minimizing Currents Mod $(q)$

Camillo De Lellis, Paul Minter, Anna Skorobogatova

We study fine structural properties related to the interior regularity of $m$ -dimensional area minimizing currents mod $(q)$ in arbitrary codimension. We show: (i) the set of points…

math.AP2024

Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents

Paul Minter, Davide Parise, Anna Skorobogatova +1

We prove that the singular set of an $m$ -dimensional integral current $T$ in $R^{n + m}$ , semicalibrated by a $C^{2, I^º_{0}}$ $m$ -form $I ¨ $ is countably $(m - 2)$ -rectifiabl…

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 $V^{n}$ in Riemannian manifolds $(N^{n + 1}, h)$ . Indeed, if…

math.DG2026

A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity

Brian Krummel, Paul Minter, Neshan Wickramasekera

Suppose $V$ is a class of stationary integral $n$ -varifolds in $B_{2}^{n + k} (0) \subset R^{n + k}$ which is closed under weak limits, homotheties, rotations, and disjoi…

math.DG2026

Minimal Surfaces with Stratified Branching Sets

Federico Franceschini, Rafe Mazzeo, Paul Minter

Inspired by the Taubes-Wu construction of $C^{1, I^\pm}$ two-valued harmonic functions by the use of symmetry, we construct minimal surfaces with stratified branching sets as…

Publications (18)

The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density 5/2

Fine Structure of Singularities in Area-Minimizing Currents Mod(q)

Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents

Quantitative Estimates on the Topology and Singular Set of Prescribed Mean Curvature Hypersurfaces

A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity

Minimal Surfaces with Stratified Branching Sets

Fine Structure of Singularities in Area-Minimizing Currents Mod $(q)$