| Résume | In this seminar, I will examine the validity of the isoperimetric inequality on manifolds with asymptotically non-negative sectional curvature. After an overview of the current state of the art on the problem, I will discuss the ABP method, originally introduced by Cabré to prove the isoperimetric inequality in Rn, and later refined by Brendle for the case of non-compact Riemannian manifolds characterized by non-negative Ricci curvature and positive asymptotic volume ratio. Finally, we will explore how this approach can be adapted to prove isoperimetric inequalities even in the presence of a small amount of negative curvature.
The results presented are part of a joint project with Stefano Pigola, Michele Rimoldi, and Giona Veronelli. |
