Research

Structure of two-dimensional mod (q) area-minimizing currents near flat singularities: the codimension one case (with A. Skorobogatova and S. Stuvard), submitted 2025

Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents (with P. Minter, D. Parise and A. Skorobogatova), submitted 2024

Fine structure of the singular set of area minimizing hypersurfaces modulo p (with C. De Lellis, J. Hirsch, A. Marchese and S. Stuvard), submitted 2022

Area minimizing hypersurfaces modulo p: a geometric free-boundary problem (with C. De Lellis, J. Hirsch, A. Marchese and S. Stuvard), JFA (2025)

Excess decay for minimizing hypercurrents mod 2Q (with C. De Lellis, J. Hirsch, A. Marchese and S. Stuvard), Nonlinear Analysis (2024)

(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents (with M. Engelstein and B. Velichkov), Geom. & Topol. (2019)

Almgren’s type Regularity for semicalibrated currents, Adv. in Math. (2019)

Regularity theory for 2-dimensional almost minimal currents III: blowup (with C. De Lellis and E. Spadaro), J. Differential Geom. (2020)

Regularity theory for 2-dimensional almost minimal currents II: branched center manifold (with C. De Lellis and E. Spadaro), Ann. PDE (2017)

Regularity theory for 2-dimensional almost minimizing currents I: Lipschitz approximation (with C. De Lellis and E. Spadaro), Trans. Amer. Math. Soc. (2018)

Uniqueness of tangent cones for 2-dimensional almost minimizing currents (with C. De Lellis and E. Spadaro), Comm. Pure Appl. Math. (2017)

Dimension of the singular set for 2-valued stationary Lipschitz graphs (with J. Hirsch), Duke Math. J. (2025)

Regularity of minimal surfaces near quadratic cones (with N. Edelen), Ann. of Math. (2023)

Singular behavior and generic regularity of min-max minimal hypersurfaces (with O. Chodosh and Y. Liokumovich), Ars Inveniendi Analytica (2022)

The singular set of minimal surfaces near polyhedral cones (with M. Colombo and N. Edelen), accepted in J. Differential Geom. (2021)

On the boundary branching set of the one-phase problem (with L. Ferreri and B. Velichkov), submitted 2024

On the fine structure of the solutions to nonlinear thin two-membrane problems in 2D (with L. Ferreri and B. Velichkov), submitted 2024

The symmetric (log-)epiperimetric inequality and a decay-growth estimate (with N. Edelen and B. Velichkov), Calc. Var. PDE (2024)

(Quasi-)conformal methods in two-dimensional free boundary problems (with G. De Philippis and B. Velichkov), J. Eur. Math. Soc. (2024)

A strong maximum principle for minimizers of the one-phase Bernoulli problem (with N. Edelen and B. Velichkov), Indiana Univ. Math. J. (2023)

Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries (with G. De Philippis, M. Engelstein and B. Velichkov), submitted 2021

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem (with M.Colombo and B. Velichkov), Interfaces and Free Boundaries (2021)

Regularity of the free-boundary for the two-phase Bernoulli problem (with G. De Philippis and B. Velichkov), Invent. Math. (2021)

On the logarithmic epiperimetric inequality for the obstacle problem (withB.Velichkov), accepted in Mathematics in Engineering (2021)

Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional (M. Engelstein and B. Velichkov), Duke Math. J (2020)

Direct epiperimetric inequalities for the thin obstacle problem and applications (with M. Colombo and B. Velichkov), Comm. Pure Appl. Math. (2019)

Free boundary regularity for a multiphase shape optimization problem (with B. Trey and B. Velichkov), Comm. PDE (2019)

A logarithmic epiperimetric inequality for the obstacle problem (with M. Colombo and B. Velichkov), Geom. Funct. Anal. Vol. (2018)

An epiperimetric inequality for the regularity of some free boundary problems: the 2-dimensional case (with B. Velichkov) Comm. Pure Appl. Math. (2018)

Carleman estimates for stationary Q-valued maps: a variational approach (with A. Halavati), submitted 2025

Unique continuation for nonlinear variational problems (with L. Ferreri and B. Velichkov), submitted 2024

Interior regularity for two-dimensional stationary Q-valued maps (with J. Hirsch), Accepted Arch. Ration. Mech. Anal (2024)

Quantitative Stability for Minimizing Yamabe Metrics (with M. Engelstein and R. Neumayer), Trans. Amer. Math. Soc. (2022)

The Riemannian Quantitative Isoperimetric Inequality (with O. Chodosh and M. Engelstein), J. Eur. Math. Soc. (2022)

On the asymptotic behavior of the solutions to parabolic variational inequalities (with M. Colombo and B. Velichkov), J. reine angew. Math. (2020)

Quantitative estimate on singularities in isoperimetric clusters (with M. Colombo), Comm. Analysis and Geom. (2019)

On the number of singular points for planar multivalued harmonic functions (with F.Ghiraldin), Manuscripta Math. (2017)