Energy quantization for Willmore surfaces with bounded index

2023/05/15 by Dorian Martino, Martino, Dorian
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2305.08668

openalex publication_date 2023/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove an energy quantization result for Willmore surfaces with bounded index, whether the underlying Riemann surfaces degenerates in the moduli space or not. To do so, we translate the question on the conformal Gauss map's point of view. In particular, we prove that in a neck or a collar region, the conformal Gauss map converges to a light-like geodesic in the De Sitter space.

Citations

• Angular Energy Quantization for Linear Elliptic Systems with\n Antisymmetric Potentials and Applications
• Variational Principles for immersed Surfaces with L²-bounded Second\n Fundamental Form

Related

• Quantization of the Willmore Energy in Riemannian Manifolds
• Energy Quantization for Willmore Surfaces and Applications
• Energy quantization for constrained Willmore surfaces
• Harmonic map methods for Willmore surfaces
• Closed surfaces with bounds on their Willmore energy