I am a mathematician interested in geometric analysis. I have been working on minimal surfaces and mean curvature flow, their variational aspects, min-max theory, and their connection with mathematical models of phase transitions - particularly the Allen-Cahn equation.
Equivariant Allen-Cahn Solutions and the Existence of Cohomogeneity 2 Minimal Surfaces (with Rayssa Caju and Jared Marx-Kuo) arXiv.org preprint: arXiv:2607.21789 [math.DG] (2026)
When can minimal hypersurfaces be connected by mean curvature flow? (with Jingwen Chen). Mathematische Annalen. 395, 40 (2026).
Volume spectrum of fiber bundles and the widths of Berger spheres (with Jingwen Chen). arXiv.org preprint: arXiv:2505.09548 [math.DG] (2025). Submitted.
Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface (with Jared Marx-Kuo). arXiv.org preprint: arXiv:2502.07098 (2025). Submitted.
Allen-Cahn equation and degenerate minimal hypersurfaces (with Jingwen Chen). Indiana University Mathematics Journal 75, 3 (2026)
Morse theory for the Allen-Cahn functional (with Jingwen Chen). Journal of Functional Analysis. 288 (9) (2025).
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). Communications in Analysis and Geometry. 31 (8), 1931-1968 (2023).
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).
The Allen-Cahn equation and variational aspects of minimal hypersurfaces. IMPA, 2018. [link]
Juan Pablo Vega Mac-Namara: Magíster en Matemática UC.
Fernanda González: Co-supervision in Magíster en Ciencias de la Ingeniería con Mención en Matemáticas Aplicadas, DIM/FCFM-Universidad de Chile. Advisor: Rayssa Caju (DIM-CMM, Universidad de Chile).
Fernando Castillo Burgos: Magíster en Matemática UC.
Rodrigo Altamirano Moreno: Co-supervision in Doctorado en Ciencias de la Ingeniería, Mención Modelación Matemática, DIM/FCFM-Universidad de Chile. Advisor: Rayssa Caju (DIM-CMM, Universidad de Chile).
Henrique Tonello Pereira: Co-supervision in Mestrado em Matemática UNICAMP. Advisor: Eder M. Correa.
Alessandra Fabian Sostisso: MATH-AmSud NETGAN project Ph.D. research stay [2026]. Advisor: Vanderson Lima.
Fernando Castillo Burgos: Taller de Iniciación Científica (Undergradute project). Monography title: Problema isoperimétrico con densidades y borbujas.
Rodrigo Altamirano Moreno: Co-supervision in Magíster en Ciencias de la Ingeniería con Mención en Matemáticas Aplicadas, DIM-Universidad de Chile. Advisor: Gabrielle Nornberg (DIM-CMM, Universidad de Chile). Thesis title: Estudio de la conjetura de Payne en dominios simplemente conexos.
Ricardo Felipe Larraín Araya: Taller de Trabajo Matemático (Undergradute project). Monography title: Superficies mínimas.
Víctor Felipe Valencia: Magíster en Matemática UC. Thesis title: Teorema de Frankel sobre variedades con borde.