# Mathematical Sciences Research Institute

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# Seminar

RAS - Research Seminar (Part 2): Isoperimetric profiles for quasi-Fuchsian manifolds September 21, 2020 (10:00 AM PDT - 11:00 AM PDT)
Parent Program: Random and Arithmetic Structures in Topology -- Virtual Semester MSRI: Online/Virtual
Speaker(s) Franco Vargas Pallete (Yale University)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

Video

#### Isoperimetric Profiles For Quasi-Fuchsian Manifolds

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25205

This is one of the research seminars for the RAS program, that distinguishes itself from the postdocs and program associates seminars in that speakers are chosen among Research Members, Research Professors with occasional outside speakers.

Abstract:

An isoperimetric profile of a Riemannian manifold is a function that for each positive number $V$ associates the optimal perimeter needed bound a volume equal to $V$. On this talk we'll see how for quasi-Fuchsian 3-manifolds this relates to Renormalized Volume (a studied functional on the deformation space). We will use this relation together with some tools from General relativity (namely the Hawking mass) to prove that, in the appropriate setup, the isoperimetric profile of an almost-Fuchsian 3-manifold stays below the profile of any Fuchsian 3-manifold, and equality occurs if and only if the manifold was Fuchsian to begin with. This is joint work with Celso Viana.