Tuesday April 29th, 2025 | |
| Time: | 4:00 PM - 5:15 PM |
| Title: | Isoperimetric Sets in Nonnegatively Curved Manifolds |
| Speaker: | Gioacchino Antonelli, NYU Courant |
| Location: | P-131 |
| Abstract: | |
| Abstract: In this talk, I will explore how the isoperimetric structure of a complete Riemannian manifold is influenced by nonnegative curvature. I will begin by presenting some positive and negative results concerning the existence of isoperimetric sets. Specifically, on a manifold with nonnegative sectional curvature and Euclidean volume growth, isoperimetric sets always exist for large volumes, but may fail to exist for small volumes. Next, I will examine the question of uniqueness for large volumes. I will show that on a manifold with nonnegative Ricci curvature, Euclidean volume growth, and quadratic curvature decay, there exists a set G of positive real numbers with density one at infinity such that, for all volumes in G, isoperimetric sets are unique. | |