2021 | Energy in Fourth Order Gravity | Rodrigo Avalos, Jorge H. Lira, Nicolas MarqueLink zum Preprint
Energy in Fourth Order Gravity
Autoren: Rodrigo Avalos, Jorge H. Lira, Nicolas Marque
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. We also exhibit examples of solutions which provide intuitions about this notion of energy which allows us to interpret it, and introduce several study cases where its analysis seems tractable. Finally, positive energy theorems are presented in restricted situations.
2020 | Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications | Yann Bernard, Paul Laurain, Nicolas MarqueLink zum Preprint
Energy Estimates for the Tracefree Curvature of Willmore Surfaces and Applications
Autoren: Yann Bernard, Paul Laurain, Nicolas Marque
We prove an ϵ-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 L2-norm.Several applications are investigated. Notably, we derive a gap statement for surfaces of the aforementioned type. We further apply our results to deduce regularity results for conformal minimal spacelike immersions into the de Sitter space S4,1.