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pro vyhledávání: '"Bernard, Yann"'
Autor:
Bernard, Yann
We discuss a large class of conformally invariant curvature energies for immersed hypersurfaces of dimension 4. The class under study includes various examples that have appeared in the recent literature and which arise from different contexts. We sh
Externí odkaz:
http://arxiv.org/abs/2402.15032
A four dimensional conformally invariant energy is studied. This energy generalises the well known two-dimensional Willmore energy. Although not positive definite, it includes minimal hypersurfaces as critical points. We compute its first variation a
Externí odkaz:
http://arxiv.org/abs/2211.05320
Autor:
Bernard, Yann
A new conformally invariant energy for four-dimensional hypersurfaces is devised. It renders possible the study of a large class of curvature energies, and we show that their critical points are smooth. As corollaries, we obtain the regularity of the
Externí odkaz:
http://arxiv.org/abs/2209.12469
We prove an $\epsilon$-regularity result for the tracefree curvature of a Willmore surface with bounded second fundamental form. For such a surface, we obtain a pointwise control of the tracefree second fundamental form from a small control of its $L
Externí odkaz:
http://arxiv.org/abs/2009.10180
We study a class of fourth-order geometric problems modelling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, bi-harmonic surfaces in the sense of Chen, among others. We prove several loc
Externí odkaz:
http://arxiv.org/abs/1811.08546
Chen's flow is a fourth-order curvature flow motivated by the spectral decomposition of immersions, a program classically pushed by B.-Y. Chen since the 1970s. In curvature flow terms the flow sits at the critical level of scaling together with the m
Externí odkaz:
http://arxiv.org/abs/1706.01707
Autor:
Bernard, Yann, Riviere, Tristan
We study ends of an oriented, immersed, non-compact, complete Willmore surfaces, which are critical points of the integral of the square of the mean curvature, in asymptotically flat spaces of any dimension; assuming the surface has $L^2$-bounded sec
Externí odkaz:
http://arxiv.org/abs/1508.01391
Akademický článek
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Publikováno v:
Bernard Yann, Wheeler Glen, Wheeler Valentina-Mira: Rigidity and stability of spheres in the Helfrich model. Interfaces Free Bound. 19 (2017), 495-523
The Helfrich functional, denoted by H^{c_0}, is a mathematical expression proposed by Helfrich (1973) for the natural free energy carried by an elastic phospholipid bilayer. Helfrich theorises that idealised elastic phospholipid bilayers minimise H^{
Externí odkaz:
http://arxiv.org/abs/1412.3533
Autor:
Bernard, Yann
Noether's theorem and the invariances of the Willmore functional are used to derive conservation laws that are satisfied by the critical points of the Willmore energy subject to generic constraints. We recover in particular previous results independe
Externí odkaz:
http://arxiv.org/abs/1409.6894