1 citations · 1 across the 12 of their papers we have counts for
12 papers
Gauge Symmetry Breaking in the Asymptotic Analysis of Self Dual Yang-Mills-Higgs Monopoles
Tristan Rivière
We consider the Self-Dual Yang Mills Higgs Lagrangian in 3 dimension. By adding a ''Gauge Mass'' term to this YMH Lagrangian in the form of norm of the connection we…
Improved Morse Index Stability for Sequences of Harmonic Maps from Degenerating Riemann Surfaces
Francesca Da Lio, Tristan Rivière, Dominik Schlagenhauf
We study the stability of the extended Morse index, defined as the number of negative and zero eigenvalues of the Jacobi operator, for sequences of harmonic maps on degenerating Ri…
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…
Weak immersions with second fundamental form in a critical Sobolev space
Dorian Martino, Tristan Rivière
We develop the analysis of Lipschitz immersions of -dimensional manifolds into having their second fundamental forms bounded in the critical Sobolev space $W^{\fr…
The Analysis of Willmore Surfaces and its Generalizations in Higher Dimensions
Tian Lan, Dorian Martino, Tristan Rivière
We review recent progress concerning the analysis of Lagrangians on immersions into depending on the first and second fundamental forms and their covariant derivativ…
The Regularity of Critical Points to Scale-Invariant Curvature Energies in Dimension 4
Yann Bernard, Tian Lan, Dorian Martino +1
We consider a class of scale-invariant curvature energies defined on immersed -dimensional manifolds and prove that weak immersions that are critical points of such energies are…
Construction of harmonic coordinates for weak immersions
Dorian Martino, Tristan Rivière
We prove that any weak immersion in the critical Sobolev space in even dimension , has global harmonic coordinates if its…
Morse Index Stability for Sequences of Sacks-Uhlenbeck Maps into a Sphere
Francesca Da Lio, Tristan Rivière, Dominik Schlagenhauf
In this paper we consider sequences of -harmonic maps, , from a closed Riemann surface into the -dimensional sphere with uniform bounded energy. These…
Coulomb Gauges and Regularity for Stationary Weak YangMills Connections in Supercritical Dimension
Riccardo Caniato, Tristan Rivière
We prove that stationary YangMills fields in dimensions 5 belonging to the variational class of weak connections are smooth away from a closed singular set of vanishing 1-di…
A Variational Theory for The Area of Legendrian Surfaces
Alessandro Pigati, Tristan Rivière
We study a new notion of critical point for the area of surfaces under the Legendrian constraint, called parametrized Hamiltonian stationary Legendrian varifolds (PHSLVs). We estab…
Conservation Laws for -Harmonic Systems with Antisymmetric Potentials and Applications
Francesca Da Lio, Tristan Rivière
We prove that -harmonic systems with antisymmetric potentials can be written in divergence form as a conservation law. This extends to the -harmonic framework the original w…
Exploring the Unknown: the Work of Louis Nirenberg on Partial Differential Equations
Tristan Rivière
Partial differential equations are central objects in the mathematical modeling of natural and social sciences (sound propagation, heat diffusion, thermodynamics, electromagnetism,…