Stability of extremal domains

Abstract: A domain in a Riemannian manifold is said to be extremal if it is a critical point of the first eigenvalue functional under volume-preserving variations. From this variational characterization, we derive a natural notion of stability. In this talk, we classify the stable extremal domains in the 2-sphere and in higher-dimensional spheres when the boundary is minimal. Additionally, we establish topological bounds for stable domains in general compact Riemannian surfaces, assuming either nonnegative total Gaussian curvature or small volume. This is joint work with Ivaldo Nunes (UFMA).

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon