19 citations · 36 across the 19 of their papers we have counts for
20 papers
A universal inequality for Neumann eigenvalues of the Laplacian on a convex domain in Euclidean space
Kei Funano
We obtain a new upper bound for Neumann eigenvalues of the Laplacian on a bounded convex domain in Euclidean space. As an application of the upper bound we derive universal inequal…
A note on domain monotonicity for the Neumann eigenvalues of the Laplacian
Kei Funano
Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obta…
Upper bounds for higher-order Poincar'e constants
Kei Funano, Yohei Sakurai
We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of…
Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
Kei Funano, Yohei Sakurai
We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal…
Macroscopic scalar curvature and areas of cycles
Hannah Alpert, Kei Funano
In this paper we prove the following. Let be an --dimensional closed hyperbolic manifold and let be a Riemannian metric on . Given an upper bound o…
Applications of the `Ham Sandwich Theorem' to eigenvalues of the Laplacian
Kei Funano
We apply Gromov's ham sandwich method to get (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant fact…