34 videos

34 videos

4 videos

4 videos

## 2022 - Francophone Computer Algebra Days - Journées nationales de calcul formel

00:00:00 / 00:00:00

## Spherical Plateau problem and applications

Appears in collection : Not Only Scalar Curvature Seminar

I will discuss an area minimization problem in certain quotients of the Hilbert sphere by countable groups. An early version of that setting appears in Besson-Courtois-Gallot’s work on the entropy inequality. As an application of this minimization problem, we obtain some stability results. For instance, consider a closed surface of genus at least $2$ endowed with a Riemannian metric $g$, and let $(S,g)$ be its universal cover. After normalizing $g$ so that the volume entropy of $(S,g)$ is $1$, it is well-known that the first eigenvalue $\lambda$ is at most $\frac14$, and equality holds if $g$ is a hyperbolic metric. The hyperbolic plane is in fact stable: if $\lambda$ is close to the upper bound $\frac14$, then $(S,g)$ is close to the hyperbolic plane in a Benjamini-Schramm topology.

### Information about the video

• Date of recording 12/9/22
• Date of publication 2/10/23
• Institution IHES
• Language English
• Audience Researchers
• Format MP4

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