6 papers
When can minimal hypersurfaces be connected by mean curvature flow?
Jingwen Chen, Pedro Gaspar
From the perspective of Morse theory, it is natural to investigate gradient flow trajectories between critical points. In this short note, we explore the minimal hypersurface analo…
Volume spectrum of fiber bundles and the widths of Berger spheres
Jingwen Chen, Pedro Gaspar
We establish that for a fiber bundle , which is a Riemannian submersion, the volume spectrum of is bounded above by the product of the volume spectrum of and th…
Allen-Cahn equation and degenerate minimal hypersurface
Jingwen Chen, Pedro Gaspar
In this short note, we present new observations and examples concerning the existence and rigidity of solutions to the Allen-Cahn equation with degenerate minimal hypersurfaces as…
Morse theory for the Allen-Cahn functional
Jingwen Chen, Pedro Gaspar
In this article, we use Morse-theoretic techniques to construct connections between low energy critical submanifolds of the Allen-Cahn energy functional in the 3-sphere via the neg…
Symmetric mean curvature flow on the n-sphere
Jingwen Chen
In this article, we generalize our previous results joint with Pedro Gaspar to higher dimensions, prove the existence of (infinitely many) eternal weak mean curvature flows in $S^{…
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…