## Publications

Below are some of the publications put out by our group.

- Azzam, Mourgoglou, Tolsa, and Volberg. On a two-phase problem for harmonic measure in general domains.
*Amer. J. Math.*, 2019 - Barceló and Carbery. On the magnitudes of compact sets in Euclidean spaces.
*Amer. J. Math.*, 2018 - Azzam, Mourgoglou, and Tolsa. Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability.
*Comm. Pure Appl. Math.*, 2017 - Dindoš, Pipher, and Rule. Boundary value problems for second-order elliptic operators satisfying a Carleson condition.
*Comm. Pure Appl. Math.*, 2017 - Dipierro, Karakhanyan, and Valdinoci. A nonlinear free boundary problem with a self-driven Bernoulli condition.
*J. Funct. Anal.*, 2017 - Azzam, Hofmann, Martell, Mayboroda, Mourgoglou, Tolsa, and Volberg. Rectifiability of harmonic measure.
*Geom. Funct. Anal.*, 2016 - Hickman. Uniform $L_x^p$–$L_{x,r}^q$ improving for dilated averages over polynomial curves.
*J. Funct. Anal.*, 2016 - Karakhanyan and Strömqvist. Estimates for capacity and discrepancy of convex surfaces in sieve-like domains with an application to homogenization.
*Calc. Var. Partial Differential Equations*, 2016 - Karakhanyan. Blaschke's rolling ball theorem and the Trudinger-Wang monotone bending.
*J. Differential Equations*, 2016 - Azzam and Tolsa. Characterization of $n$-rectifiability in terms of Jones' square function: Part II.
*Geom. Funct. Anal.*, 2015 - Carbery and Valdimarsson. The endpoint multilinear Kakeya theorem via the Borsuk-Ulam theorem.
*J. Funct. Anal.*, 2013 - Azzam and Schul. Hard Sard: quantitative implicit function and extension theorems for Lipschitz maps.
*Geom. Funct. Anal.*, 2012 - Colliander and Oh. Almost sure well-posedness of the cubic nonlinear Schrödinger equation below $L^2(\Bbb T)$.
*Duke Math. J.*, 2012 - Dindoš and Wall. The $L^p$ Dirichlet problem for second-order, non-divergence form operators: solvability and perturbation results.
*J. Funct. Anal.*, 2011 - Dendrinos and Wright. Fourier restriction to polynomial curves I: a geometric inequality.
*Amer. J. Math.*, 2010 - Blue and Soffer. Phase space analysis on some black hole manifolds.
*J. Funct. Anal.*, 2009 - Dendrinos, Laghi, and Wright. Universal $L^p$ improving for averages along polynomial curves in low dimensions.
*J. Funct. Anal.*, 2009 - Chaudhuri and Karakhanyan. On derivation of Euler-Lagrange equations for incompressible energy-minimizers.
*Calc. Var. Partial Differential Equations*, 2009 - Bennett, Carbery, Christ, and Tao. The Brascamp-Lieb inequalities: finiteness, structure and extremals.
*Geom. Funct. Anal.*, 2008 - Dindos, Petermichl, and Pipher. The $L^p$ Dirichlet problem for second order elliptic operators and a $p$-adapted square function.
*J. Funct. Anal.*, 2007 - Karakhanyan, Kenig, and Shahgholian. The behavior of the free boundary near the fixed boundary for a minimization problem.
*Calc. Var. Partial Differential Equations*, 2007 - Bennett, Carbery, and Tao. On the multilinear restriction and Kakeya conjectures.
*Acta Math.*, 2006 - Karakhanyan. Up-to boundary regularity for a singular perturbation problem of $p$-Laplacian type.
*J. Differential Equations*, 2006 - Cowling, Dorofaeff, Seeger, and Wright. A family of singular oscillatory integral operators and failure of weak amenability.
*Duke Math. J.*, 2005 - Seeger, Tao, and Wright. Singular maximal functions and Radon transforms near $L^1$.
*Amer. J. Math.*, 2004 - Barceló, Bennett, and Carbery. A bilinear extension inequality in two dimensions.
*J. Funct. Anal.*, 2003 - Tao and Wright. $L^p$ improving bounds for averages along curves.
*J. Amer. Math. Soc.*, 2003 - Carbery, Wainger, and Wright. Double Hilbert transforms along polynomial surfaces in $R^3$.
*Duke Math. J.*, 2000 - Bournaveas. A new proof of global existence for the Dirac Klein-Gordon equations in one space dimension.
*J. Funct. Anal.*, 2000 - Carbery, Christ, and Wright. Multidimensional van der Corput and sublevel set estimates.
*J. Amer. Math. Soc.*, 1999 - Wainger, Wright, and Ziesler. Singular integrals associated to hypersurfaces: $L^2$ theory.
*J. Funct. Anal.*, 1999 - Carbery, Vance, Wainger, and Wright. A variant of the notion of a space of homogeneous type.
*J. Funct. Anal.*, 1995 - Carbery, Wainger, and Wright. Hilbert transforms and maximal functions associated to flat curves on the Heisenberg group.
*J. Amer. Math. Soc.*, 1995 - Carbery, Vance, Wainger, and Watson. The Hilbert transform and maximal function along flat curves, dilations, and differential equations.
*Amer. J. Math.*, 1994 - Carbery, Romera, and Soria. Radial weights and mixed norm inequalities for the disc multiplier.
*J. Funct. Anal.*, 1992 - Wright. $L^p$ estimates for operators associated to oscillating plane curves.
*Duke Math. J.*, 1992 - Carbery, Christ, Vance, Wainger, and Watson. Operators associated to flat plane curves: $L^p$ estimates via dilation methods.
*Duke Math. J.*, 1989 - Carbery. The boundedness of the maximal Bochner-Riesz operator on $L^{4}({\bf R}^{2})$.
*Duke Math. J.*, 1983