| Résume | Taking advantage of monotone quantities along geometric flow to derive
functional inequalities is a recurring scheme in geometric analysis.
Recently, we have provided a unified perspective on a broad range of
monotonicity formulas in both linear and nonlinear potential theory, as well as
along the inverse mean curvature flow. The quantities involved in this study are
generalizations and variants of the Willmore functional.
In the talk I will focus on the implications of these formulas and present
Willmore-type inequalities in Rn and in Riemannian manifolds with suitable
bounds on the Ricci curvature.
Based on joint works with Luca Benatti, Marco Pozzetta, and Stefano Mannella.
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