Ian Fleschler

collaborators

5 papers

math.AP2025

An essential one sided boundary singularity for a $3$ -dimensional area minimizing current in $R^{5}$

Ian Fleschler

We construct a $3$ -dimensional area minimizing current $T$ in $R^{5}$ whose boundary contains a real analytic surface of multiplicity $2$ at which $T$ has a density $1$ esse…

math.AP2025

On the uniqueness of tangent cones to area minimizing currents at boundaries with arbitrary multiplicity

Ian Fleschler

We consider an area minimizing current $T$ in a $C^{2}$ submanifold $I^£$ of $R^{m + n}$ , with arbitrary integer boundary multiplicity $\partial T = Q [[I^]]$ where $I^$ i…

math.AP2025

On the regularity of area minimizing currents at boundaries with arbitrary multiplicity

Ian Fleschler, Reinaldo Resende

In this paper, we consider an area minimizing integral $m$ -current $T$ within a submanifold $I^£$ of $R^{m + n}$ , taking a boundary $I^$ with arbitrary multiplicity $Q \in \m…

math.AP2024

Allard-type regularity theory for area minimizing currents at boundaries with arbitrary multiplicity

Ian Fleschler

This is an announcement of a series of upcoming works on boundary regularity for area minimizing currents, one of which is in collaboration with Reinaldo Resende. The setting we co…

math.AP2024

Faber-Krahn inequalities, the Alt-Caffarelli-Friedman formula, and Carleson's $ε^{2}$ conjecture in higher dimensions

Ian Fleschler, Xavier Tolsa, Michele Villa

The main aim of this article is to prove quantitative spectral inequalities for the Laplacian with Dirichlet boundary conditions. More specifically, we prove sharp quantitative sta…

An essential one sided boundary singularity for a 3-dimensional area minimizing current in R5

On the uniqueness of tangent cones to area minimizing currents at boundaries with arbitrary multiplicity

On the regularity of area minimizing currents at boundaries with arbitrary multiplicity

Allard-type regularity theory for area minimizing currents at boundaries with arbitrary multiplicity

Faber-Krahn inequalities, the Alt-Caffarelli-Friedman formula, and Carleson's ε2 conjecture in higher dimensions

An essential one sided boundary singularity for a $3$ -dimensional area minimizing current in $R^{5}$

Faber-Krahn inequalities, the Alt-Caffarelli-Friedman formula, and Carleson's $ε^{2}$ conjecture in higher dimensions