F. Ghiraldin, L. Spolaor:
On the number of singular points for planar multivalued harmonic functions
Manuscripta Math. (Accepted Paper) 2016
M. Colombo, L. Spolaor:
Quantitative estimate on singularities in isoperimetric clusters
CAG (Accepted Paper) 2017
L. Spolaor, B. Velichkov:
An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case
Comm. Pure Appl. Math. (Accepted Paper) p. 32, 2017
M. Colombo, L. Spolaor, B. Velichkov:
A logarithmic epiperimetric inequality for the obstacle problem
Geom. Funct. Anal. (Accepted Paper) 2017
C. De Lellis, E. Spadaro, L. Spolaor:
Regularity theory for $2$-dimensional almost minimal currents II: branched center manifold
Ann. PDE Vol. 2, N. 18, p. 85 pp, 2017
C. De Lellis, E. Spadaro, L. Spolaor:
Uniqueness of tangent cones for $2$-dimensional almost minimizing currents
Comm. Pure Appl. Math. Vol. 70, N. 7, p. 14021421, 2017
M. Colombo, N. Edelen, L. Spolaor:
The singular set of minimal surfaces near polyhedral cones
JDG (Accepted Paper) 2017
M. Colombo, L. Spolaor, B. Velichkov:
Direct epiperimetric inequalities for the thin obstacle problem and applications
Comm. Pure Appl. Math. (Accepted Paper) 2017
C. De Lellis, E. Spadaro, L. Spolaor:
Regularity theory for $2$-dimensional almost minimal currents I: Lipschitz approximation
Transactions AMS Vol. 370, N. 3, p. 17831801, 2018
L. Spolaor:
Almgren's type regularity for Semicalibrated Currents
Adv. Math. (Accepted Paper) 2018
M. Engelstein, L. Spolaor, B. Velichkov:
(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents
Geom. Topol. (Accepted Paper) 2018
L. Spolaor, B. Trey, B. Velichkov:
Free boundary regularity for a multiphase shape optimization problem
Communications in Partial Differential Equations (Accepted Paper) 2018
M. Colombo, L. Spolaor, B. Velichkov:
On the asymptotic behavior of the solutions to parabolic variational inequalities
J. Reine Agnew. Math. (Accepted Paper) 2018
M. Engelstein, L. Spolaor, B. Velichkov:
Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional
Duke Math. J. (Accepted Paper) 2018
O. Chodosh, M. Engelstein, L. Spolaor:
The Riemannian quantitative isoperimetric inequality
(Submitted Paper) 2019
N. Edelen, L. Spolaor:
Regularity of minimal surfaces near quadratic cones
(Submitted Paper) 2019
C. De Lellis, E. Spadaro, L. Spolaor:
Regularity theory for $2$-dimensional almost minimal currents III: blowup
J. Differential Geom. Vol. 116, N. 1, p. 125-185, 2020
O. Chodosh, Y. Liokumovich, L. Spolaor:
Singular behavior and generic regularity of min-max minimal hypersurfaces
(Preprint) 2020
M. Colombo, L. Spolaor, B. Velichkov:
Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem
Interfaces and Free Boundaries (Accepted Paper) 2021
G. De Philippis, M. Engelstein, L. Spolaor, B. Velichkov:
Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries
(Preprint) 2021
G. De Philippis, L. Spolaor, B. Velichkov:
Regularity of the free boundary for the two-phase Bernoulli problem
Inventiones mathematicae 2021
C. De Lellis, J. Hirsch, A. Marchese, L. Spolaor, S. Stuvard:
Area minimizing hypersurfaces modulo $p$: a geometric free-boundary problem
(Submitted Paper) 2021
L. Spolaor, B. Velichkov:
On the logarithmic epiperimetric inequality for the obstacle problem
Mathematics in Engineering Vol. 3, p. 1--42, 2021
G. De Philippis, L. Spolaor, B. Velichkov:
(Quasi-)conformal methods in two-dimensional free boundary problems
J. Eur. Math. Soc. (Accepted Paper) 2021
N. Edelen, L. Spolaor, B. Velichkov:
A strong maximum principle for minimizers of the one-phase Bernoulli problem
Indiana Math. J. (Accepted Paper) 2022
C. De Lellis, J. Hirsch, A. Marchese, L. Spolaor, S. Stuvard:
Fine structure of the singular set of area minimizing hypersurfaces modulo $p$
(Submitted Paper) 2022
N. Edelen, L. Spolaor, B. Velichkov:
The symmetric (log-)epiperimetric inequality and a decay-growth estimate
(Preprint) 2023
C. De Lellis, J. Hirsch, A. Marchese, L. Spolaor, S. Stuvard:
Excess decay for minimizing hypercurrents mod $2Q$
(Submitted Paper) 2023