Biharmonic submanifolds represent an influential area in Riemannian geometry, where the concept of harmonic maps is extended to a fourth-order setting. A submanifold is deemed biharmonic when its ...

Riemann titled his lecture on the topic, presented in 1854, “On the Hypotheses which Lie at the Foundations of Geometry.” In that lecture, Riemann cut to the core of Euclidean geometry ...

Over the last decades, it has been used to prove several significant conjectures in Riemannian geometry and topology (in dimension three). In this project we focus on Ricci flow in higher dimensions, ...