activity
20242026
most citedFractional Sobolev spaces on Riemannian manifolds

1 citations · 1 across the 5 of their papers we have counts for

collaborators

7 papers

math.AP2026

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…

math.AP2026

The stability conjecture for the Bernoulli problem in dimension four

Xavier Fernández-Real, Joaquim Serra

We prove that every global classical stable solution to the one-phase Bernoulli problem in is one-dimensional. In particular, if nonempty, its free boundary consists…

math.DG2026

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…

math.AP2026

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…

math.AP2025

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…

math.AP2025

Global Stable Solutions to the Free Boundary Allen--Cahn and Bernoulli Problems in 3D are One-Dimensional

Hardy Chan, Xavier Fernández-Real, Alessio Figalli +1

A long-standing conjecture of De Giorgi asserts that every monotone solution of the Allen--Cahn equation in is one-dimensional if . A stronger version…

math.AP2024★ 1 cited

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…