1 citations · 2 across the 7 of their papers we have counts for
10 papers
Stable solutions of the Allen--Cahn equation in dimension three are one-dimensional
Hardy Chan, Xavier Fernández-Real, Alessio Figalli +2
We prove that every bounded stable solution of the Allen--Cahn equation in is one-dimensional. As a consequence, this shows the validity of De Giorgi's conjecture for…
Universal completeness of exponentials
Susanna Bertolini, Enric Florit-Simon, Lukas Liehr +1
We consider generalizations of the classical Fourier uniqueness theorem. First, we construct a family of uniformly discrete sets , of uniform density one, such…
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…
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…
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…
Fractional Sobolev spaces on Riemannian manifolds
Michele Caselli, Enric Florit-Simon, Joaquim Serra
This article studies the canonical Hilbert energy on a Riemannian manifold for , with particular focus on the case of closed manifolds. Several equivalent d…
Yau's conjecture for nonlocal minimal surfaces
Michele Caselli, Enric Florit-Simon, Joaquim Serra
We introduce nonlocal minimal surfaces on closed manifolds and establish a far-reaching Yau-type result: in every closed, -dimensional Riemannian manifold we construct infinitel…