5 citations · 10 across the 5 of their papers we have counts for
7 papers
Equivariant Allen--Cahn Solutions and the Existence of Cohomogeneity Minimal Surfaces
Rayssa Caju, Pedro Gaspar, Jared Marx-Kuo
We develop a regularity theory for equivariant Allen--Cahn solutions on closed Riemannian manifolds with a Lie group acting isometrically. When the cohomogeneity of the action is b…
Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere
Jingwen Chen, Pedro Gaspar
In this article we study eternal solutions to the Allen-Cahn equation in the 3-sphere, in view of the connection between the gradient flow of the associated energy functional, and…
Ground states of semilinear elliptic equations
Rayssa Caju, Pedro Gaspar, Marco A. M. Guaraco +1
We study solutions of , where the potential can have an arbitrary number of wells at arbitrary heights, including bottomless wells with subcritical decay. In our…
Solutions of the Allen-Cahn equation on closed manifolds in the presence of symmetry
Rayssa Caju, Pedro Gaspar
We prove that given a minimal hypersurface in a compact Riemannian manifold without boundary, if all the Jacobi fields of are generated by ambient isometries, then we c…
The Weyl Law for the phase transition spectrum and density of limit interfaces
Pedro Gaspar, Marco A. M. Guaraco
We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich-Marques-Neves. As an application we give phase transition adaptations of the proofs of…
The second inner variation of energy and the Morse index of limit interfaces
Pedro Gaspar
In this article we study the second variation of the energy functional associated to the Allen-Cahn equation on closed manifolds. Extending well known analogies between the gradien…
The Allen-Cahn equation on closed manifolds
Pedro Gaspar, Marco A. M. Guaraco
We study global variational properties of the space of solutions to on any closed Riemannian manifold . Our techniques are inspired by recent advanc…