INTERESTS IN RESEARCH

My investigation is centered in the quasiconformal world, as well as in geometric function theory and elliptic partial differential equations. I am also interested in similar problems in the Heisenberg groups, as well as questions of geometric measure theory, and harmonic and complex analysis. Some keywords are: quasiregular mappings, quasiconformal mappings, Beltrami equation, elliptic equations, divergence form equations, inverse problems, Helmholtz equation, analytic capacity, singular integrals, removable sets, Hausdorff measure, nonlinear potential theory, mappings of finite distortion.

PhD THESIS

My PhD thesis is called "Removable singularities for planar quasiregular mappings", and i defended it at the Departament de Matemàtiques of the Universitat Autònoma de Barcelona, in 20th november 2006.

PUBLICATIONS

"Removable singularities for Hölder continuous quasiregular mappings in the plane" Ann. Acad. Sci. Fenn. Math. 32 (2007), no. 1, 171-178.

"Nonremovable sets for Hölder continuous quasiregular mappings in the plane" Michigan Math. J. 55 (2007), no. 1, 195-208.

"Improved Painlevé removability for bounded planar quasiregular mappings", with K. Astala, J. Mateu, J. Orobitg and I. Uriarte-Tuero, Harmonic analysis, partial differential equations, and related topics, 1-12, Contemp. Math., 428, Amer. Math. Soc., Providence, RI, 2007.

"Distortion of Hausdorff measures and improved Painlevé removability for bounded quasiregular mappings", with K. Astala, J. Mateu, J. Orobitg and I. Uriarte-Tuero, Duke Math. J. 141 (2008), no. 3, 539-571.

"Beltrami equations with coefficient in the Sobolev space W1,p", with D. Faraco, J. Mateu, J. Orobitg and X. Zhong, Publ. Mat. 53 (2009), no. 1, 197-230

"Sharp nonremovability examples for Hölder continuous quasiregular mappings in the plane", with I. Uriarte-Tuero, J. Anal. Math. 108 (2009), 171-188.

"Analytic capacity and quasiconformal mappings with W1,2 Beltrami coefficient", with X. Tolsa, Math. Res. Lett. 15 (2008), no. 4, 779-793.

"Orlicz-Sobolev regularity for mappings with subexponentially integrable distortion", with P. Koskela, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 20 (2009), no. 4, 301-326.

"Stability of Calderón inverse conductivity problem in the plane for discontinuous conductivities", with D. Faraco and A. Ruiz, Inverse Probl. Imaging 4 (2010), no. 1, 49-91.

"Uniqueness of normalized homeomorphic solutions of nonlinear Beltrami equations", with K. Astala, D. Faraco, J. Jääskeläinen and L. Székelyhidi, Int. Math. Res. Not. IMRN 2012, no. 18, 4101Ð4119.

"Quasiconformal distortion of Riesz capacities and Hausdorff measures", with K. Astala, X. Tolsa, I. Uriarte-Tuero and J. Verdera, Amer. J. Math. (2013).

"Weighted estimates for Beltrami equations", with V. Cruz, Ann. Acad. Sci. Fenn. Math. (2013).

"Mappings with Finite Distortion in $L^p_loc$ : Modulus of Continuity and Compression of Hausdorff Measure", with D. Herron, to be published at Isr. J. Math.

" Mappings with subexponentially integrable distortion: modulus of continuity, and distortion of Hausdorff measure and Minkowski content", with D. Herron, submitted.