29 citations · 91 across the 12 of their papers we have counts for
9 papers · 1 filter
Regularity of four dimensional Willmore-type hypersurfaces
Peter Olamide Olanipekun, Yann Bernard
A four dimensional conformally invariant energy is studied. This energy generalises the well known two-dimensional Willmore energy. Although not positive definite, it includes mini…
A New Conformal Invariant for four-Dimensional Hypersurfaces
Yann Bernard
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 criti…
Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications
Yann Bernard, Paul Laurain, Nicolas Marque
We prove an -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 t…
Analysis of the Inhomogeneous Willmore Equation
Yann Bernard, Glen Wheeler, Valentina-Mira Wheeler
We study a class of fourth-order geometric problems modelling Willmore surfaces, conformally constrained Willmore surfaces, isoperimetrically constrained Willmore surfaces, bi-harm…
Concentration-compactness and finite-time singularities for Chen's flow
Yann Bernard, Glen Wheeler, Valentina-Mira Wheeler
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 te…
Ends of Immersed Minimal and Willmore Surfaces in Asymptotically Flat Spaces
Yann Bernard, Tristan Riviere
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 fl…