Analysis and Mathematical Physics
Existence and Regularity of Nonlocal Minimal Surfaces
In the '80s, Yau conjectured that every closed Riemannian 3-manifold contains infinitely many smooth minimal hypersurfaces. In this talk, I will present a Yau-type existence result for nonlocal minimal surfaces and discuss how one can recover the classical Yau's conjecture from it. The main tools are min-max methods for the fractional perimeter and a compactness/regularity theory for the associated critical points, which gives smoothness in low dimensions and a small singular set in higher dimensions. Time permitting, I will discuss a broader program about extending these ideas to higher codimension.
Date & Time
March 23, 2026 | 2:30pm – 3:30pm
Add to calendar
03/23/2026 14:30
03/23/2026 15:30
Analysis and Mathematical Physics
use-title
Topic: Existence and Regularity of Nonlocal Minimal Surfaces
Speakers: Michele Caselli, Princeton University
More: https://www.ias.edu/math/events/analysis-and-mathematical-physics-78
In the '80s, Yau conjectured that every closed Riemannian 3-manifold
contains infinitely many smooth minimal hypersurfaces. In this talk, I
will present a Yau-type existence result for nonlocal minimal surfaces
and discuss how one can recover the classical Yau's conjecture from
it. The main tools are min-max methods for the fractional perimeter
and a compactness/regularity theory for the associated critical
points, which gives smoothness in low dimensions and a small singular
set in higher dimensions. Time permitting, I will discuss a broader
program about extending these ideas to higher codimension.
Simonyi Hall 101 and Remote Access
a7a99c3d46944b65a08073518d638c23
Location
Simonyi Hall 101 and Remote AccessSpeakers
Michele Caselli, Princeton University