Full Professor, UCSD

Email: lspolaor AT ucsd.edu

Home-page: https://sites.google.com/ucsd.edu/lucaspolaor

Available papers (34):

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• A. Halavati - L. Spolaor (Preprint)
  Carleman estimates for stationary $Q$-valued maps: a variational approach (2025)
• A. Skorobogatova - L. Spolaor - S. Stuvard (Preprint)
  Structure of two-dimensional mod$(q)$ area minimizing currents near flat singularities: the codimension one case (2025)
• 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)
• G. De Philippis - L. Spolaor - B. Velichkov (Inventiones mathematicae)
  Regularity of the free boundary for the two-phase Bernoulli problem (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)
• 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)
• 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)
• O. Chodosh - M. Engelstein - L. Spolaor (JEMS)
  The Riemannian quantitative isoperimetric inequality (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:

• 8 jun 2026 - 12 jun 2026: International geometric analysis conference in Milan II
• 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