9 papers
On the vortex filament conjecture for the Gross-Pitaevskii equation
Manuel del Pino, Rowan Juneman, Monica Musso +1
We establish one form of the vortex filament conjecture for the three-dimensional Gross-Pitaevskii equation. Given any smooth closed embedded binormal flow of curves on a compact t…
A Bernstein problem for translating solutions to the mean curvature flow
Juan Davila, Manuel del Pino, Juncheng Wei
We study entire graphical translating solutions of the mean curvature flow, \[ \operatorname{div}\!\left(\frac{\nabla G}{\sqrt{1+|\nabla G|^2}}\right) =\frac{1}{\sqrt{1+|\nabla G|^…
The double sphere solution in the liquid drop model
Manuel del Pino, Rupert L. Frank, Monica Musso
We consider the problem of finding critical domains for the energy functional $$ \mathcal E (Ω) = {\rm Per}\,(Ω) + \frac 12 \iint_{Ω\times Ω} \frac{dx\,dy}{…
Nondegeneracy and Morse Index of Ginzburg--Landau Vortices
Manuel del Pino, Yong Liu, Monica Musso +2
We prove that the standard degree-two and degree-three vortex solutions of the Ginzburg-Landau equation are nondegenerate. Their Morse indices are also computed. The proof relies o…
A two-dimensional Allen-Cahn theory for interfaces with boundary
Marco Badran, Manuel del Pino, Marco A. M. Guaraco
We develop a two-dimensional Allen-Cahn theory for interfaces with boundary in the line-bundle framework introduced by Fröhlich and Struwe. The central new object is a model soluti…
Collapsing-tube type II blow-up for the energy-supercritical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei +1
We construct a new type II finite-time blow-up mechanism for the energy-supercritical heat equation \[ u_t=Δu+u^3, \qquad n\geq 5. \] The solution is positive and blows up only at…