Research
My research interests lie among Partial Differential Equations, Geometric Analysis, and the Calculus of Variations.Publications
Regularity for non-local almost minimal boundaries and applications, with N. Guillen, submitted.
Global Regularity for Semilinear Reaction-Diffusion Systems with Super-Quadratic Nonlinearities, with A. Vasseur, preprint.
Global Regularity of Solutions to Systems of Reaction-Diffusion with Sub-Quadratic Growth in any dimension with A. Vasseur, Communications in PDEs, Volume 34, Issue 10, 2009, pages 1228--1250, pdf
Highly Degenerate Harmonic Mean Curvature Flow, with P. Daskalopoulos, Calculus of Variations and PDEs, Volume 35, Issue 3, 2009, 365--384, pdf
On the evolution of weakly convex hyper-surfaces by the $Q_k$ flow in any dimension N with P. Daskalopoulos and N. Sesum, Communications in PDEs, Volume 35, Issue 03, 2010, pdf
Minimally invasive surgery for Ricci flow singularities with S. Angenent and D. Knopf, to appear on J. Reine Angew. Math., pdf
Time Scales: from Nabla Calculus to Delta Calculus and vice versa via Duality, International Journal of Difference Equations, Volume 5, Issue 1, 2010, pdf
Highly Degenerate Harmonic Mean Curvature Flow Ph.D. Thesis, pdf