Geometry Seminar: A. Pluda

Speaker: Alessandra Pluda, University of Pisa<

Title: From linear potential theory to the inverse mean curvature flow

Abstract: This talk explores a unified family of monotonicity formulas arising from distinct contexts in geometric analysis. We first examine formulas within linear potential theory, pioneered by Colding (2012) and Colding-Minicozzi (2014). We then contrast these with the monotonicity of the Hawking mass along the Inverse Mean Curvature Flow (IMCF), as established by Huisken and Ilmanen (2001). The bridge between these frameworks is found in the geometric quantities associated with the level sets of $p$-harmonic functions, where the IMCF formally emerges as the limit case $p \to 1$. I will discuss the rigorous mathematical framework required to establish this connection, the analytical tools developed for this purpose, and their applications to geometric problems -specifically focusing on a pinching theorem for 3-manifolds.