Tristan Rivière

activity

20242026

collaborators

10 papers

math.AP2026

Gauge Symmetry Breaking in the Asymptotic Analysis of Self Dual Yang-Mills-Higgs $S U (2)$ Monopoles

Tristan RiviÃ¨re

We consider the $S U (2)$ Self-Dual Yang Mills Higgs Lagrangian in 3 dimension. By adding a ''Gauge Mass'' term to this YMH Lagrangian in the form of $L^{2}$ norm of the connection we…

math.DG2026

Improved Morse Index Stability for Sequences of Harmonic Maps from Degenerating Riemann Surfaces

Francesca Da Lio, Tristan RiviÃ¨re, 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…

math.DG2026

The Analysis of Willmore Surfaces and its Generalizations in Higher Dimensions

Tian Lan, Dorian Martino, Tristan RiviÃ¨re

We review recent progress concerning the analysis of Lagrangians on immersions into $R^{d}$ depending on the first and second fundamental forms and their covariant derivativ…

math.AP2026

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 $4$ -dimensional manifolds and prove that weak immersions that are critical points of such energies are…

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…

math.DG2025

Weak immersions with second fundamental form in a critical Sobolev space

Dorian Martino, Tristan RiviÃ¨re

We develop the analysis of Lipschitz immersions of $n$ -dimensional manifolds into $R^{d}$ having their second fundamental forms bounded in the critical Sobolev space $W^{\fr…