24 citations · 91 across the 19 of their papers we have counts for
7 papers · 1 filter
Strong convexity for harmonic functions on compact symmetric spaces
Gabor Lippner, Dan Mangoubi, Zachary McGuirk +1
Let be a harmonic function defined on a spherical disk. It is shown that is nonnegative for all where is the Laplace-Beltrami operator. This f…
Bounded multiplicity for eigenvalues of a circular vibrating clamped plate
Yuri Lvovsky, Dan Mangoubi
We prove that no eigenvalue of the clamped disk can have multiplicity greater than six. Our method of proof is based on a new recursion formula, linear algebra arguments and a tran…
The Volume of a Local Nodal Domain
Dan Mangoubi
Let M either be a closed real analytic Riemannian manifold or a closed smooth Riemannian surface. We estimate from below the volume of a nodal domain component in an arbitrary ball…
Tubular Neighborhoods of Nodal Sets and Diophantine Approximation
Dmitry Jakobson, Dan Mangoubi
We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold M. As an…
Local Asymmetry and the Inner Radius of Nodal Domains
Dan Mangoubi
Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue λ. We show that the volume of {f>0}…
On the Inner Radius of Nodal Domains
Dan Mangoubi
Let M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue λ. We give upper and lower bounds on the inner radius of the type C/λ^k…