Robert and Elaine Phelps Professor, appointed 1996 (Ph.D. Stanford 1992)
On leave: Spring '13
Research area: Analysis, geometric measure theory
Personal Web page: http://www.math.washington.edu/~toro/
Office: PDL C-343
My research interests include geometric measure theory, harmonic analysis and partial
differential equations. I apply techniques from these fields to study free boundary
regularity problems with very rough boundary data. These problems arise naturally in
physics and engineering, where the free boundary may appear as the interface between a
fluid and the air, or water and ice. I have also worked in the problem of constructing
good parameterization for sets satisfying some minimal geometric requirements (for
Reifenberg parameterizations for sets with holes (with G. David), Memoirs of the AMS, 215,
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.
On the smoothness of Hölder-doubling measures (with D. Preiss and X. Tolsa), Calculus of
Variations and PDEs 35 (2009), 339--363.
A new approach to absolute continuity of elliptic measure, with applications to
non-symmetric equations, (with C. Kenig, H. Koch and J. Pipher), Adv. Math. 153, 2000, no. 2, 231--298.
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.
Surfaces with generalized second fundamental form in L2 are Lipschitz
manifolds, J. Differential Geometry, 39, 1994, 65--101.