Research

I am a mathematician interested in geometric analysis. I have been working on minimal surfaces, their variational aspects, min-max theory, and their connection with mathematical models of phase transitions - particularly the Allen-Cahn equation.

Publications and preprints

• Allen-Cahn equation and degenerate minimal hypersurface (with Jingwen Chen). arXiv.org preprint:arXiv:2402.18799 (2024).

• Morse theory for the Allen-Cahn functional (with Jingwen Chen). arXiv.org preprint: arxiv:2310.17096 [math.DG] (2023). Submitted.

• Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere (with Jingwen Chen). The Journal of Geometric Analysis  33, 283 (2023).

• Ground states of semilinear elliptic problems with applications to the Allen–Cahn equation on the sphere (with Rayssa Caju, Marco A. M. Guaraco, and Henrik Matthiesen). Calculus of Variations and Partial Differential Equations 61, 71 (2022).

• Solutions of the Allen-Cahn equation on closed manifolds in the presence of symmetry (with Rayssa Caju). To appear in Communications in Analysis and Geometry. [arXiv preprint]

• The Weyl Law for the phase transition spectrum and density of limit interfaces (with Marco A. M. Guaraco). Geometric and Functional Analysis 29, 382-410 (2019). 

• The second inner variation of energy and the Morse index of limit interfaces. The Journal of Geometric Analysis 30, 69-85 (2020). 

• The Allen–Cahn equation on closed manifolds (with Marco A. M. Guaraco). Calculus of Variations and Partial Differential Equations 57 (4), 101 (2018).

Ph.D. thesis

The Allen-Cahn equation and variational aspects of minimal hypersurfaces. IMPA, 2018. [link]