6 papers
Shift of the Bose-Einstein condensation transition in the presence of a second atomic species
Pedro M. Gaspar, Vanderlei S. Bagnato, Patricia C. M. Castilho
Atomic interactions play an important role in the properties of ultracold atomic gases. In single component bosonic systems, its effect is already present at the critical point for…
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…
Infinitely Many Surfaces with Prescribed Mean Curvature in the Presence of a Strictly Stable Minimal Surface
Pedro Gaspar, Jared Marx-Kuo
We construct infinitely many distinct hypersurfaces with prescribed mean curvature (PMC) for a large class of prescribing functions when is a closed smooth manifold…
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…