Carlos RománPostdoctoral researcher in mathematics

Research interests: My research interests lie primarily in the calculus of variations and nonlinear partial differential equations. I have focused on the Ginzburg-Landau model of superconductivity, mathematical biology, and conformal geometry. The common point in my diverse research interests is about the analysis of singularities in elliptic equations.

Publications in Refereed Journals

  1. (with A. Pistoia) Large conformal metrics with prescribed scalar curvature, J. Differential Equations 263 (2017), no. 9, 5902−5938.
  2. [pdf file, arXiv version, journal version]
  3. (with M. del Pino, M. Musso, and J. Wei) Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3, Accepted for publication in J. Anal. Math.
  4. [pdf file, arXiv version]
  5. (with M. del Pino) Large conformal metrics with prescribed sign-changing Gauss curvature, Calc. Var. Partial Differential Equations 54 (2015), no. 1, 763−789.
  6. [pdf file, arXiv version, journal version]

Submitted Papers

  1. 3D vortex approximation construction and ε-level estimates for the Ginzburg-Landau functional.
  2. [pdf file, arXiv version]
  3. (with D. Bonheure and J.-B. Casteras) Unbounded mass radial solutions for the Keller-Segel equation in the disk.
  4. [pdf file, arXiv version]