5 citations · 10 across the 9 of their papers we have counts for
11 papers
Morse Index Stability of Branched Willmore Immersions
Alexis Michelat
We show that the sum of the Morse index and the nullity of Willmore immersions of bounded energy is lower semi-continuous without assuming that the limiting immersion and the bubbl…
Morse Index Stability of Biharmonic Maps in Critical Dimension
Alexis Michelat
Furthering the development of Da Lio-Gianocca-Rivière's Morse stability theory (arXiv:2212.03124) that was first applied to harmonic maps between manifolds and later extended to th…
Weighted Eigenvalue Problems for Fourth-Order Operators in Degenerating Annuli
Alexis Michelat, Tristan Rivière
We obtain a nigh optimal estimate for the first eigenvalue of two natural weighted problems associated to the bilaplacian (and of a continuous family of fourth-order elliptic opera…
Morse Index Stability of Willmore Immersions I
Alexis Michelat, Tristan Rivière
In a recent work, F. Da Lio, M. Gianocca, and T. Rivière developped a new method to show upper semi-continuity results in geometric analysis, which they applied to conformally inva…
The Loewner Energy via the Renormalised Energy of Moving Frames
Alexis Michelat, Yilin Wang
We obtain a new formula for the Loewner energy of Jordan curves on the sphere, which is a Kähler potential for the essentially unique Kähler metric on the Weil-Petersson universal…
Higher Regularity of Weak Limits of Willmore Immersions I
Alexis Michelat, Tristan Rivière
We obtain in arbitrary codimension a removability result on the order of singularity of weak limits and bubbles of Willmore immersions measured by the second residue. This permits…
Higher Regularity of Weak Limits of Willmore Immersions II
Alexis Michelat, Tristan Rivière
We obtain in arbitrary codimension a removability result on the order of singularity of Willmore surfaces realising the width of Willmore min-max problems on spheres. As a conseque…
Computer-Assisted Proof of the Main Theorem of 'The Classification of Branched Willmore Spheres in the -Sphere and the -Sphere'
Alexis Michelat, Tristan Rivière
We provide a computer-assisted proof of the holomorphy of the quartic and the octic meromorphic differentials arising in the main Theorem 4.11 of our paper 'The Classification of B…
The Classification of Branched Willmore Spheres in the -Sphere and the -Sphere
Alexis Michelat, Tristan Rivière
We extend the classification of Robert Bryant of Willmore spheres in to variational branched Willmore spheres and show that they are inverse stereographic projections o…
Morse Index of Willmore spheres in
Alexis Michelat
We obtain an upper bound for the Morse index of Willmore spheres coming from an immersion of . The quantization of Willmore energy shows that there exists an in…
A Viscosity Method for the Min-Max Construction of Closed Geodesics
Alexis Michelat, Tristan Rivière
We present a viscosity approach to the min-max construction of closed geodesics on compact Riemannian manifolds of arbitrary dimension. We also construct counter-examples in dimens…