18 citations · 90 across the 21 of their papers we have counts for
24 papers
Morse index stability for p-Yang-Mills connections
Mario Gauvrit, Paul Laurain, Tristan Rivière
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…
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…
Morse index stability for Yang-Mills connections
Mario Gauvrit, Paul Laurain
We prove stability results of the Morse index plus nullity of Yang-Mills connections in dimension 4 under weak convergence. Precisely we establish that the sum of the Morse indices…
Concentration of CMC Surfaces in a 3-manifold
Paul Laurain
We prove that simply connected H-surfaces with small diameter in a 3-manifold necessarily concentrate at a critical point of the scalar curvature.
Asymptotic analysis for surfaces with large constant mean curvature and free boundaries
Paul Laurain
We prove that simply connected H-surfaces with bounded area and free boundary in a domain necessarily concentrate at a critical point of the mean curvature of the boundary of this…
Stability of the Pohožaev obstrucion in dimension 3
Olivier Druet, Paul Laurain
We investigate problems connected to the stability of the wellknown Pohožaev obstruction. We generalize results which were obtained in the minimizing setting by Brezis and Nirenber…
An Obstruction to the Existence of Immersed Curves of Prescribed Curvature
Stephane Kirsch, Paul Laurain
Here are the proofs of your article. You can submit your corrections online or by fax. For online submission please insert your corrections in the online correc…
Fine multibubble analysis in the higher-dimensional Brezis-Nirenberg problem
Tobias König, Paul Laurain
For a bounded set and a perturbation , we analyze the concentration behavior of a blow-up sequence of positive solutions to \[ -Δu_ε+…
Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions
Tobias König, Paul Laurain
For a smooth bounded domain and smooth functions and , we consider the asymptotic behavior of a sequence of positive solutions to $-Δu_ε+ (a+εV)…
Rigidity Theorems for Asymptotically Euclidean -singular Spaces
Rodrigo Avalos, Paul Laurain, Nicolas Marque
In this paper we prove some rigidity theorems associated to -curvature analysis on asymptotically Euclidean (AE) manifolds, which are inspired by the analysis of conservation pr…
Existence of Ginzburg-Landau minimizers with optimal boundary data and applications
PAul Laurain, Romain Petrides
We perform the classical Ginzburg-Landau analysis originated from the celebrated paper by Bethuel, Brezis, Hélein for optimal boundary data. More precisely, we give optimal regular…
Constant -curvature metrics with a singularity
Tobias König, Paul Laurain
For dimensions , we classify singular solutions to the generalized Liouville equation on with the finite integral c…
On the Positive Energy Theorem for Stationary Solutions to Fourth-Order Gravity
Rodrigo Avalos, Paul Laurain, Jorge Lira
In this paper we prove a positive energy theorem related to fourth-order gravitational theories, which is a higher-order analogue of the classical ADM positive energy theorem of ge…
Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications
Yann Bernard, Paul Laurain, Nicolas Marque
We prove an -regularity result for the tracefree curvature of a Willmore surface with bounded second fundamental form. For such a surface, we obtain a pointwise control of the t…
Classification of uniformly distributed measures of dimension in general codimension
Paul Laurain, Mircea Petrache
Starting with the work of Preiss on the geometry of measures, the classification of uniform measures in has remained open, except for and for compactly supporte…
Existence of Min-Max Free Boundary Disks Releasing the Width of a Manifold
Paul Laurain, Romain Petrides
We perform a replacement procedure in order to produce a free boundary minimal surface whose area achieves the min-max value over all disk sweepouts of a manifold whose boundary li…
Energy convexity of intrinsic bi-harmonic maps and applications I: spherical target
Paul Laurain, Longzhi Lin
Every harmonic map is an intrinsic bi-harmonic map as an absolute minimizer of the intrinsic bi-energy functional, therefore intrinsic bi-harmonic map and its heat flow are more ge…
A Pohozaev-type formula and Quantization of Horizontal Half-Harmonic Maps
Francesca Da Lio, Paul Laurain, Tristan Rivière
In a recent paper the first and the third authors introduced the notion of horizontal α-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of th…
Energy Quantization of Willmore surfaces at the boundary of the Moduli Space
Paul Laurain, Tristan Rivière
We establish an energy quantization result for sequences of Willmore surfaces when the underlying sequence of Riemann surfaces is degenerating in the moduli space. we notably exhib…
Regularity and quantification for harmonic maps with free boundary
Paul Laurain, Romain Petrides
We prove a quantification result for harmonic maps with free boundary from arbitrary Riemannian surfaces into the unit ball of with bounded energy. This general…
Concentration of small Willmore spheres in Riemannian 3-manifolds
Paul Laurain, Andrea Mondino
Given a 3-dimensional Riemannian manifold , we prove that if is a sequence of Willmore spheres (or more generally area-constrained Willmore spheres), having Willmore…
Optimal estimate for the gradient of Green functions on degenerating surfaces and applications
Paul Laurain, Tristan Rivière
In this paper we prove a uniform estimate for the gradient of the Green function on a closed Riemann surface, independent of its conformal class, and we derive compactness results…
Energy quantization for biharmonic maps
P. Laurain, T. Riviere
In the present work we establish an energy quantization (or energy identity) result for solutions to scaling invariant variational problems in dimension 4 which includes biharmonic…
Angular Energy Quantization for Linear Elliptic Systems with Antisymmetric Potentials and Applications
Paul Laurain, Tristan Riviere
In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schrödinger type with antisymmetric potential…