[spolaor]

Assistant Professor, UCSD

**Email:** *lspolaor AT ucsd.edu*

- L. Ferreri - L. Spolaor - B. Velichkov (preprint)

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

On the boundary branching set of the one-phase problem (2024) - L. Ferreri - L. Spolaor - B. Velichkov (preprint)

Unique continuation for nonlinear variational problems (2024) - P. Minter - D. Parise - A. Skorobogatova - L. Spolaor (Preprint)

Rectifiability of the singular set and uniqueness of tangent cones for semicalibrated currents (2024) - C. De Lellis - J. Hirsch - A. Marchese - L. Spolaor - S. Stuvard (
*Nonlinear Anal.*)

Excess decay for minimizing hypercurrents mod $2Q$ (2024) - N. Edelen - L. Spolaor - B. Velichkov (
*Indiana Univ. Math. J.*)

A strong maximum principle for minimizers of the one-phase Bernoulli problem (2024) - G. De Philippis - L. Spolaor - B. Velichkov (
*J. Eur. Math. Soc.*)

(Quasi-)conformal methods in two-dimensional free boundary problems (2024) - N. Edelen - L. Spolaor - B. Velichkov (
*Calculus of Variations and Partial Differential Equations*)

The symmetric (log-)epiperimetric inequality and a decay-growth estimate (2023) - C. De Lellis - J. Hirsch - A. Marchese - L. Spolaor - S. Stuvard (Submitted Paper)

Fine structure of the singular set of area minimizing hypersurfaces modulo $p$ (2022) - G. De Philippis - M. Engelstein - L. Spolaor - B. Velichkov (Preprint)

Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries (2021) - C. De Lellis - J. Hirsch - A. Marchese - L. Spolaor - S. Stuvard (Submitted Paper)

Area minimizing hypersurfaces modulo $p$: a geometric free-boundary problem (2021) - L. Spolaor - B. Velichkov (
*Mathematics in Engineering*)

On the logarithmic epiperimetric inequality for the obstacle problem (2021) - G. De Philippis - L. Spolaor - B. Velichkov (
*Inventiones mathematicae*)

Regularity of the free boundary for the two-phase Bernoulli problem (2021) - M. Colombo - L. Spolaor - B. Velichkov (
*Interfaces and Free Boundaries*)

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem (2021) - C. De Lellis - E. Spadaro - L. Spolaor (
*J. Differential Geom.*)

Regularity theory for $2$-dimensional almost minimal currents III: blowup (2020) - O. Chodosh - Y. Liokumovich - L. Spolaor (Preprint)

Singular behavior and generic regularity of min-max minimal hypersurfaces (2020) - M. Colombo - L. Spolaor - B. Velichkov (
*Comm. Pure Appl. Math.*)

Direct epiperimetric inequalities for the thin obstacle problem and applications (2020) - M. Engelstein - L. Spolaor - B. Velichkov (
*Duke Math. J.*)

Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional (2020) - M. Colombo - L. Spolaor - B. Velichkov (
*J. Reine Angew. Math.*)

On the asymptotic behavior of the solutions to parabolic variational inequalities (2020) - O. Chodosh - M. Engelstein - L. Spolaor (Submitted Paper)

The Riemannian quantitative isoperimetric inequality (2019) - N. Edelen - L. Spolaor (Submitted Paper)

Regularity of minimal surfaces near quadratic cones (2019) - M. Engelstein - L. Spolaor - B. Velichkov (
*Geom. Topol.*)

(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents (2019) - L. Spolaor - B. Velichkov (
*Comm. Pure Appl. Math.*)

An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case (2019) - C. De Lellis - E. Spadaro - L. Spolaor (
*Transactions AMS*)

Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation (2018) - L. Spolaor (Accepted Paper:
*Adv. Math.*)

Almgren's type regularity for Semicalibrated Currents (2018) - L. Spolaor - B. Trey - B. Velichkov (
*Communications in Partial Differential Equations*)

Free boundary regularity for a multiphase shape optimization problem (2018) - M. Colombo - L. Spolaor - B. Velichkov (
*Geom. Funct. Anal.*)

A logarithmic epiperimetric inequality for the obstacle problem (2018) - M. Colombo - L. Spolaor (Accepted Paper:
*CAG*)

Quantitative estimate on singularities in isoperimetric clusters (2017) - C. De Lellis - E. Spadaro - L. Spolaor (
*Ann. PDE*)

Regularity theory for $2$-dimensional almost minimal currents II: branched center manifold (2017) - C. De Lellis - E. Spadaro - L. Spolaor (
*Comm. Pure Appl. Math.*)

Uniqueness of tangent cones for $2$-dimensional almost minimizing currents (2017) - M. Colombo - N. Edelen - L. Spolaor (Accepted Paper:
*JDG*)

The singular set of minimal surfaces near polyhedral cones (2017) - F. Ghiraldin - L. Spolaor (Accepted Paper:
*Manuscripta Math.*)

On the number of singular points for planar multivalued harmonic functions (2016)

*17 jun 2024 - 21 jun 2024:*Geometric Measure Theory and applications 2024*29 may 2023 - 2 jun 2023:*Geometric Measure Theory, Bressanone 2023*8 jun 2022 - 10 jun 2022:*Geometric Analysis and PDE on Garda Lake*3 sep 2018 - 6 sep 2018:*Meeting on Applied Mathematics and Calculus of Variations*26 jun 2017 - 30 jun 2017:*Curves and Networks in Geometric Analysis

*22 mar 2019 - 24 mar 2019:*New Trends in Geometric Measure Theory