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I work in Geometric Analysis. So far, I have been mainly interested in problems with a variational nature such as the existence of minimal hypersurfaces or the behavior of solutions to semilinear PDEs in general manifolds. An example of these is the relation between the stationary Allen-Cahn equation (a PDE arising in the theory of Phase Transitions) and minimal hypersuraces (critical points of the area functional). As mathematical objects the former is, in some sense, more analytical while the later is more geometrical. However, they usually present parallel behaviours that allow us to understand one by means of the other.


(j/w Pedro Gaspar) The Allen-Cahn equation on closed manifolds. arXiv preprint arXiv:1608.06575 (2016). (Submmited)

Min-max for phase transitions and the existence of embedded minimal hypersurfaces. arXiv preprint arXiv: 1505.06698 (2015). (Accepted for publication on Journal of Differential Geometry)