8 papers
Improvement of flatness in annuli
Xavier Fernández-Real, Enric Florit-Simon, Joaquim Serra
We present a short and flexible improvement-of-flatness argument adapted to the setting of exterior domains, where one is naturally led to work with annuli instead of balls. As a m…
Finite index solutions to the Bernoulli problem in three dimensions are axially symmetric
Xavier Fernández-Real, Enric Florit-Simon, Joaquim Serra
We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in is axially symmetric. In fact, we additionally pr…
Equivalence of intrinsic and extrinsic area bounds for minimal surfaces
Enric Florit-Simon
We show that intrinsic and extrinsic area density bounds are equivalent, with matching asymptotic values, for complete, connected, smooth minimal immersions …
Phase transitions with bounded index: Parallels to De Giorgi's conjecture
Enric Florit-Simon
A well-known conjecture of De Giorgi -- motivated by analogy with the Bernstein problem for minimal surfaces -- asserts the rigidity of monotone solutions to the Allen--Cahn equati…
Weyl Law and convergence in the classical limit for min-max nonlocal minimal surfaces
Enric Florit-Simon
We study nonlocal minimal surfaces as a new approximation theory for the area functional, and more specifically in the context of Yau's conjecture on the existence of minimal surfa…
On stable solutions to the Allen-Cahn equation with bounded energy density in
Enric Florit-Simon, Joaquim Serra
We show that stable solutions to the Allen-Cahn equation with bounded energy density (or equivalently, with cubic energy growth) are one-dimensional. Thi…