Event
Antoine M茅tras , Universit茅 de Montr茅al
Higher-order Cheeger inequalities for Laplacian and Steklov eigenvalues.
Cheeger鈥檚 inequality is a lower bound for the Laplacian鈥檚 first eigenvalue on a manifold depending only a geometric constant called Cheeger鈥檚 constant. I will present a higher-order Cheeger inequality for compact manifold without boundaries, giving a lower bound for higher eigenvalues using a natural generalisation of Cheeger鈥檚 constant. This result is adapted from the proof by Lee, Gharan and Trevissan [1] of this inequality for the discrete Laplacian on graphs. I will also apply their methods to prove a similar inequality for Steklov eigenvalues.聽聽