P. Laurain

collaborators

5 papers

math.DG2026

Rigidity Theorems for Asymptotically Euclidean $Q$ -singular Spaces

Rodrigo Avalos, Paul Laurain, Nicolas Marque

In this paper we prove some rigidity theorems associated to $Q$ -curvature analysis on asymptotically Euclidean (AE) manifolds, which are inspired by the analysis of conservation pr…

math.AP2025

Fine multibubble analysis in the higher-dimensional Brezis-Nirenberg problem

Tobias KÃ¶nig, Paul Laurain

For a bounded set $I^c ◯ \subset R^{N}$ and a perturbation $V \in C^{1} (I^c ◯)$ , we analyze the concentration behavior of a blow-up sequence of positive solutions to \[ -Îu_…

math.AP2025

Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions

Tobias KÃ¶nig, Paul Laurain

For a smooth bounded domain $I^c ◯ \subset R^{3}$ and smooth functions $a$ and $V$ , we consider the asymptotic behavior of a sequence of positive solutions $u_{I^} µ$ to $-Îu_Îµ+ (a…

math.DG2025

Huber Theorem revisited in dimensions 2 and 4

Paul Laurain, Dorian Martino

We study the second Huber theorem in dimensions 2 and 4. In dimension 2, we prove a new version assuming that the Gauss curvature lies in a negative Sobolev space using Coulomb fra…

math.DG2025

Morse index stability for p-Yang-Mills connections

Mario Gauvrit, Paul Laurain, Tristan RiviÃ¨re

We establish the lower semi continuity of the Morse index and the upper continuity of the Morse Index plus nullity of sequences of critical points of the Sacks-Uhlenbeck type relax…