Uniform Regularity Results for Critical and Subcritical Surface Energies

2017/11/21 by Yann, Bernard, Rivière, Tristan · 1 citation
#35G50 #35R01 #49Q10 #53A05 #58E12 #58J05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.07686

Abstract

We establish regularity results for critical points to energies of immersed surfaces depending on the first and the second fundamental form exclusively. These results hold for a large class of intrinsic elliptic Lagrangians which are sub-critical or critical. They are derived using uniform ε-regularity estimates which do not degenerate as the Lagrangians approach the critical regime given by the Willmore integrand

Cited by

• Stability of the Morse Index for the p-harmonic Approximation of Harmonic Maps into Homogeneous Spaces

Related

• Regularity theory for tangent-point energies: The non-degenerate\n sub-critical case
• Critical weak immersed Surfaces within Sub-manifolds of the Teichmüller Space
• The Regularity of Critical Points to Scale-Invariant Curvature Energies in Dimension 4
• Analysis of Critical Points of Conformally Invariant Curvature Energies in 4d
• Regularity at the free boundary for Dirac-harmonic maps from surfaces