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Luca Spolaor
[spolaor]
Assistant Professor, UCSD
Email:
lspolaor
AT
ucsd.edu
Available papers (32):
[plain text]
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)
Seminars:
11 jan 2017:
A direct approach to an epiperimetric inequality for Free-Boundary problems
Speaker:
23 jun 2025 - 27 jun 2025:
International geometric analysis conference in Milan
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
Organizer:
22 mar 2019 - 24 mar 2019:
New Trends in Geometric Measure Theory
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