Seminar of the HSE–Skoltech Laboratory of Representation Theory and Mathematical Physics. Speaker: Tianyu Ma

Abstract: Functionals defined on Riemannian metrics on compact surfaces whose critical points are induced by free boundary minimal immersions (FBMI) into geodesic balls in the upper hemispheres of Sⁿ or into Hⁿ were introduced by Lima, Menezes, and Medvedev. In our paper, we generalize their method to higher dimensions. We present some functionals Θᵣ,ᵢ, Ωᵣ,ᵢ whose formulae involve Steklov eigenvalues defined on Riemannian metrics on a compact manifold Σᵏ with boundary. We show that the critical points of Θᵣ,ᵢ with 0 < r < π/2 (resp., Ωᵣ,ᵢ with r > 0) are metrics induced by an FBMI into a suitably located geodesic ball Bⁿ(r) in Sⁿ (resp., Hⁿ), with a mild assumption on the hyperbolic case. We also present a new functional Ξ⁺ᵣ,ᵢ defined using Laplacian eigenvalues whose critical metrics are also induced by FBMI's into geodesic balls into the upper hemisphere.

The seminar will take place at the Faculty of Mathematics on February 20, at 16:20, room 326. 

Information about past seminars is available here: https://sites.google.com/site/alexandrburyakhomepage/lab-seminar?authuser=0