We study the umbilic points of Willmore surfaces in codimension 1 from the viewpoint of the conformal Gauss map. We first study the local behaviour of the conformal Gauss map near umbilic curves and prove that they are geodesics up to a conformal transformation if and only if the Willmore immersion is, up to a conformal transformation, the gluing of minimal surfaces in the 3-dimensional hyperbolic space.
In this paper we make a detailed analysis of conservation principles in the context of a family of fourth-order gravitational theories generated via a quadratic Lagrangian. In particular, we focus on the associated notion of energy and start a program related to its study.
An intrinsic $\varepsilon$-regularity for the tracefree curvature of Willmore immersions. We apply it to show gap lemmas and a Lorentz estimates for minimal surfaces in the de Sitter space.
ARMA 2023.
In this paper we prove some rigidity theorems associated to Q-curvature analysis on asymptotically Euclidean (AE) manifolds, which are inspired by the analysis of conservation principles within fourth order gravitational theories.
In the present paper, we study the coupled Einstein Constraint Equations (ECE) on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. In particular, we do not impose any specific model for infinity.
A study of minimal Willmore bubbling. First example of Willmore bubbling.
Published IMRN, 2020.
An explicit study of the conformal Gauss map and its application to Willmore surfaces. Concluded with a study of conformally minimal surfaces.
Potential Analysis 2020.
An $\varepsilon$-regularity result on the mean curvature of Willmore surfaces, and first applications to Willmore minimal bubbling.
Preprint 2019.