Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere

J Chen, P Gaspar - The Journal of Geometric Analysis, 2023 - Springer
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 the …

The Parabolic U (1)-Higgs Equations and Codimension-Two Mean Curvature Flows

D Parise, A Pigati, D Stern - Geometric and Functional Analysis, 2024 - Springer
The Parabolic U(1)-Higgs Equations and Codimension-Two Mean Curvature Flows | Geometric
and Functional Analysis Skip to main content SpringerLink Account Menu Find a journal …

Mean Curvature Flow on the Three-Sphere

J Chen - 2023 - search.proquest.com
In this thesis 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 the …

Second-Order Estimates for Transition Layers and a Curvature Estimate for the Parabolic Allen–Cahn

H The Nguyen, S Wang - International Mathematics Research …, 2024 - academic.oup.com
Abstract The parabolic Allen–Cahn equation is a semilinear partial differential equation that
is closely linked to the mean curvature flow by a singular perturbation. Motivated by the work …