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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…