Papers and Preprints

• Surfaces with generalized second fundamental form in $L^{2}$ are Lipschitz manifolds, J. Differential Geometry, 39, (1994), 65-101.

• Geometric conditions and existence of bilipschitz parameterizations, Duke Mathematical Journal, 77, (1995), 193-227.

• Compactness Properties of Weakly p-Harmonic Maps into Homogeneous Spaces, with C.Y. Wang, Indiana Univ. Math. J., 44, (1995), 87-113.

• Harmonic Measure on Locally Flat Domains, with C. Kenig, Duke Mathematical Journal, 87, (1997), 509-551.

• Doubling and Flatness: Geometry of Measures, Notices of the AMS, 44, (1997), 1087-1094.

• Free Boundary Regularity for Harmonic Measures and Poisson Kernels, with C. Kenig, Annals of Math. 150, (1999), 369-454.

• Reifenberg Flat Metric Spaces, Snowballs and Embeddings, with G. David, Math. Ann., 315, (1999), 641-720.

• Square Functions and Harmonic Measure for Elliptic Equations, with C. Kenig, H. Koch and J. Pipher, Adv. Math. 153 (2000), no. 2, 231--298.

• Asymptotically optimally doubling measures and Reifenberg flat sets with vanishing constant, with G. David and C. Kenig, Comm. Pure Appl. Math. 54, (2001), 385-449.

• Free Boundary Regularity for the Poisson Kernel below the Continuous Threshold with C. Kenig, Math. Research Letters, 9 (2002), 1-7.

• Poisson Kernel Characterization of Reifenberg Flat Chord Arc Domains with C. Kenig, Ann. Scient. Ec. Norm. Sup. 36, (2003), 323-401.

• On the free boundary regularity theorem of Alt and Caffarelli with C. Kenig, Discrete and Continuous Dynamical Systems 10, (2004), 397-422.

• Free boundary regularity below the continuous threshold: 2-phase problems with C. Kenig, J. Reine. Angew. Math. 596, (2006), 1-44.

• Stability of Lewis and Vogel's result with D. Preiss, Revista Matematica Iberoamericana 23, (2007), 17-55.

• A generalization of Reifenberg's theorem in $R^3$ with G. David, T. DePauw, GAFA 18, (2008), 1168-1235.

• Geometry of Measures: Harmonic Analysis meets Geometric Measure Theory, Handbook of geometric analysis. No. 1, 449-465, Adv. Lect. Math. (ALM), 7, Int. Press, Somerville, MA, (2008).

• On the smoothness of H\"older doubling measures with D. Preiss and X. Tolsa, Calculus of Variations and PDE's 35 (2009), 339-363.

• Boundary Structure and size in terms of interior and exterior harmonic measures in higher dimensions with C. Kenig and D. Preiss, J. Amer. Math. Soc. 22 (2009), 771-796.

• Divergence form operators in Reifenberg flat domains with E. Milakis, Mathematische Zeitschrift 264 (2010), 15-41. .

• The Cauchy problem for Schr\"odinger flows into K\"ahler manifolds with C. Kenig, T. Lamm, D. Pollack and G. Staffilani, Discrete and Continuous Dynamical Systems 27, (2010), 389-439.

• Potential Analysis meets Geometric Measure Theory, Proceedings of ICM 2010, III.

• Reifenberg parameterizations for sets with holes with G. David, Memoirs of the AMS, 215, (2012).

• Harmonic Analysis on Chord Arc Domains with E. Milakis and J. Pipher, J. Geom. Anal. 23 (2013) .

• Quasisymmetry and rectifiability of quasispheres with M. Badger, J. Gill and S. Rohde, Trans. Amer. Math. Soc. 336 (2014).

• Perturbation of elliptic operators in chord arc domains with E. Milakis and J.Pipher, Contemporary Mathematics (Amer. Math. Soc.) 612 (2014).

• Regularity of Almost Minimizers with Free Boundary, with G. David, to appear in Calculus of Variations and PDEs.

• Rectifiability via a square function and Preiss' theorem, with X. Tolsa, to appear in International Mathematics Research Notices 2014; doi: 10.1093/imrn/rnu082.

• Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps with J. Azzam and M. Badger, submitted.

• A new characterization of chord-arc domains, with J. Azzam, S. Hofmann, J.M. Martell and K. Nystro\"om, to appear in JEMS.

• Wasserstein Distance and the Rectifiability of Doubling Measures: Part I, with J. Azzam and G. David, to appear in Mathematische Annalen.

• Square Functions and the $A_\infty$ Property of Elliptic Measures, with C. Kenig, B. Kirchheim, and J. Pipher, to appear in The Journal of Geometric Analysis, (DOI) 10.1007/s12220-015-9630-6

• Wasserstein Distance and the Rectifiability of Doubling Measures: Part II, with J. Azzam and G. David, Mathematische Zeitschrift, 286 (2017), 861-891.

• Structure of sets which are well approximated by zero sets of harmonic polynomials, with M. Badger and M. Engelstein, Analysis \& PDE 10-6 (2017), 1455--1495. DOI 10.2140/apde.2017.10.1455

• $A_\infty$ implies NTA for a class of variable coefficient elliptic operators with S. Hofmann and J.M. Martell,to appear in Journal of Differential Equations.

• Boundary rectifiability and elliptic operators with $W^{1,1}$ coefficients with Z. Zhao,to appear in Advances in Calculus of Variations.

• Free boundary regularity for almost-minimizers, with G. David and M. Engelstein, to appear in Advances in Mathematics.

• Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part I: The small constant case with S. Hofmann, J.M. Martell, S. Mayboroda, and Z. Zhao.

• Regularity of the singular set in a two-phase problem for harmonic measure with H\"older data with M. Badger and M. Engelstein,

• Characterization of rectifiable measures in terms of $\alpha$-numbers with J. Azzam and X. Tolsa

• Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition with M. Akman, S. Hofmann and J.M. Martell.

• Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates with J. Cavero, S. Hofmann, J.M. Martell

• Two Phase Free Boundary Problem for Poisson Kernels with S. Bortz, M.Engelstein, M. Goering, and Z. Zhao.

• Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case with S. Hofmann, J.M. Martell, S. Mayboroda, and Z. Zhao.

• Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals with David, M. Engelstein, M. Smit-Vega-Garcia.