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pro vyhledávání: '"Michelat, Alexis"'
Autor:
Michelat, Alexis
Furthering the development of Da Lio-Gianocca-Rivi\`ere's Morse stability theory (arXiv:2212.03124) that was first applied to harmonic maps between manifolds and later extended to the case of Willmore immersions (arXiv:2306.04608-04609), we generalis
Externí odkaz:
http://arxiv.org/abs/2312.07494
Autor:
Michelat, Alexis, Rivière, Tristan
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 operators in dimension $2$) in degenerating annuli (that are central object
Externí odkaz:
http://arxiv.org/abs/2306.04609
Autor:
Michelat, Alexis, Rivière, Tristan
In a recent work, F. Da Lio, M. Gianocca, and T. Rivi\`ere developped a new method to show upper semi-continuity results in geometric analysis, which they applied to conformally invariant Lagrangians in dimension $2$ (that include harmonic maps). In
Externí odkaz:
http://arxiv.org/abs/2306.04608
Autor:
Michelat, Alexis, Mondino, Andrea
We show that the quantization of energy for Willmore spheres into closed Riemannian manifolds holds provided that the Willmore energy and the area are uniformly bounded. The analogous energy quantization result holds for Willmore surfaces of arbitrar
Externí odkaz:
http://arxiv.org/abs/2112.13831
Autor:
Michelat, Alexis, Wang, Yilin
We obtain a new formula for the Loewner energy of Jordan curves on the sphere, which is a K\"ahler potential for the essentially unique K\"ahler metric on the Weil-Petersson universal Teichm\"uller space, as the renormalised energy of moving frames o
Externí odkaz:
http://arxiv.org/abs/2111.14748
Autor:
Michelat, Alexis
We develop a general method to compute the Morse index of branched Willmore spheres and show that the Morse index is equal to the index of certain matrix whose dimension is equal to the number of ends of the dual minimal surface. As a corollary, we f
Externí odkaz:
http://arxiv.org/abs/1905.05742
Autor:
Michelat, Alexis
We study the moduli space of null curves in Klein's quartic in the four-dimensional (complex) projective plane using methods developed by Robert Bryant. As a consequence, we show that minimal surfaces with $9$ embedded planar ends do not exist and fo
Externí odkaz:
http://arxiv.org/abs/1905.04942
Autor:
Michelat, Alexis, Rivière, Tristan
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 consequence, out of the twelve families of non-planar minimal surfaces in $\ma
Externí odkaz:
http://arxiv.org/abs/1904.09957
Autor:
Michelat, Alexis
We show that the sum of the Morse indices of the Willmore spheres realising the width of Willmore type sweep-outs is bounded by the number of the parameters of the min-max. As an application, we deduce that among the true Willmore spheres realising t
Externí odkaz:
http://arxiv.org/abs/1808.07700
Autor:
Michelat, Alexis
We show that in viscous approximations of functionals defined on Finsler manifolds, it is possible to construct suitable sequences of critical points of these approximations satisfying the expected Morse index bounds as in Lazer-Solimini's theory, to
Externí odkaz:
http://arxiv.org/abs/1806.09578