Paul Minter

activity

20212026

most citedA Structure Theory for Stable Codimension 1 Integral Varifolds with Applications to Area Minimising Hypersurfaces mod p

8 citations · 19 across the 12 of their papers we have counts for

collaborators

12 papers

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

An Optimal Regularity Theory for Immersed Stable Minimal Hypersurfaces with Small Singular Set

Paul Minter, Zhengyi Xiao

We show that if $M^{n}$ is a properly immersed, two-sided, stable minimal hypersurface in $B_{1}^{n + 1} (0) ∖ S$ , where $S$ is closed with $H^{n - 2} (S) = 0$ , then $\text{di…

math.DG2026

Area minimising hypersurfaces mod $p$ do not admit immersed branch points

Paul Minter, Sidney Stanbury

We show that area minimising hypersurfaces mod $p$ do not admit immersed branch points, namely branch points about which all classical singularities are immersed. Furthermore, we s…

math.DG2025

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes

Spencer Becker-Kahn, Paul Minter, Neshan Wickramasekera

We study stationary integral $n$ -varifolds $V$ in the unit ball $B_{1} (0) \subset R^{n + k}$ . Allard's regularity theorem establishes the existence of $ε = ε (n, k) \in (0, 1)$ for w…

math.AP2024★ 1 cited

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 $C^{2, κ_{0}}$ $m$ -form $ω$ is countably $(m - 2)$ -rectifiable.…

math.AP2024★ 1 cited

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.AP2023

The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and $H^{m - 2}$ -a.e. Uniqueness of Tangent Cones

Camillo De Lellis, Paul Minter, Anna Skorobogatova

We consider an area-minimizing integral current $T$ of codimension higher than 1 ins a smooth Riemannian manifold $Σ$ . We prove that $T$ has a unique tangent cone, which is a super…

math.DG2022★ 3 cited

The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density $Q + 1/2$

Paul Minter

For each positive integer $Q \in Z_{\geq 2}$ , we prove a multi-valued $C^{1, α}$ regularity theorem for varifolds in the class $S_{Q}$ , i.e., stable codimension one s…

math.DG2022

Quantitative Estimates on the Singular Set of Minimal Hypersurfaces with Bounded Index

Nicolau S. Aiex, Sean McCurdy, Paul Minter

We prove local measure bounds on the tubular neighbourhood of the singular set of codimension one stationary integral $n$ -varifolds $V$ in Riemannian manifolds which have both: (i)…

math.DG2021★ 8 cited

A Structure Theory for Stable Codimension 1 Integral Varifolds with Applications to Area Minimising Hypersurfaces mod p

Paul Minter, Neshan Wickramasekera

For any $Q \in {\frac{3}{2}, 2, \frac{5}{2}, 3, \dots}$ , we establish a structure theory for the class $S_{Q}$ of stable codimension 1 stationary integral varifolds admitting…

math.DG2021★ 3 cited

A Campanato Regularity Theory for Multi-Valued Functions with Applications to Minimal Surface Regularity Theory

Paul Minter

The regularity theory of the Campanato space $L_{k}^{(q, λ)} (Ω)$ has found many applications within the regularity theory of solutions to various geometric variational probl…

math.DG2021★ 3 cited

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…

A Branch Set Stratification for Stationary Varifolds with Epsilon-Regularity

An Optimal Regularity Theory for Immersed Stable Minimal Hypersurfaces with Small Singular Set

Area minimising hypersurfaces mod p do not admit immersed branch points

On the Nature of Stationary Integral Varifolds near Multiplicity 2 Planes

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

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

The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and Hm−2-a.e. Uniqueness of Tangent Cones

The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density Q+1/2

Quantitative Estimates on the Singular Set of Minimal Hypersurfaces with Bounded Index

A Structure Theory for Stable Codimension 1 Integral Varifolds with Applications to Area Minimising Hypersurfaces mod p

A Campanato Regularity Theory for Multi-Valued Functions with Applications to Minimal Surface Regularity Theory

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

Area minimising hypersurfaces mod $p$ do not admit immersed branch points

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

The Fine Structure of the Singular Set of Area-Minimizing Integral Currents III: Frequency 1 Flat Singular Points and $H^{m - 2}$ -a.e. Uniqueness of Tangent Cones

The Structure of Stable Codimension One Integral Varifolds near Classical Cones of Density $Q + 1/2$