24 citations · 30 across the 2 of their papers we have counts for
5 papers
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…
Spectral Flexibility of Symplectic Manifolds T^2 x M
Dan Mangoubi
We consider Riemannian metrics compatible with the natural symplectic structure on T^2 x M, where T^2 is a symplectic 2-Torus and M is a closed symplectic manifold. To each such me…
Riemann Surfaces and 3-Regular Graphs
Dan Mangoubi
In this thesis we consider a way to construct a rich family of compact Riemann Surfaces in a combinatorial way. Given a 3-regualr graph with orientation, we construct a finite-area…