[spolaor]

Assistant Professor, UCSD

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

- M. Colombo - L. Spolaor - B. Velichkov (Preprint)

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem (2019) - 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) - G. De Philippis - L. Spolaor - B. Velichkov (Preprint)

Regularity of the free boundary for the two-phase Bernoulli problem (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) - M. Engelstein - L. Spolaor - B. Velichkov (Accepted Paper:
*Geom. Topol.*)

(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents (2018) - L. Spolaor - B. Trey - B. Velichkov (Accepted Paper:
*Communications in Partial Differential Equations*)

Free boundary regularity for a multiphase shape optimization problem (2018) - M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*J. Reine Agnew. Math.*)

On the asymptotic behavior of the solutions to parabolic variational inequalities (2018) - M. Engelstein - L. Spolaor - B. Velichkov (Accepted Paper:
*Duke Math. J.*)

Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional (2018) - M. Colombo - L. Spolaor (Accepted Paper:
*CAG*)

Quantitative estimate on singularities in isoperimetric clusters (2017) - C. De Lellis - E. Spadaro - L. Spolaor (Accepted Paper:
*JDG*)

Regularity theory for $2$-dimensional almost minimal currents III: blowup (2017) - L. Spolaor - B. Velichkov (Accepted Paper:
*Comm. Pure Appl. Math.*)

An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case (2017) - M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*Geom. Funct. Anal.*)

A logarithmic epiperimetric inequality for the obstacle problem (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 - L. Spolaor - B. Velichkov (Accepted Paper:
*Comm. Pure Appl. Math.*)

Direct epiperimetric inequalities for the thin obstacle problem and applications (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)

*3 sep 2018 - 6 sep 2018:*Meeting on Applied Mathematics and Calculus of Variations

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