8 citations · 14 across the 7 of their papers we have counts for
11 papers
Optimal stretching for lattice points under convex curves
Sinan Ariturk, Richard S. Laugesen
Suppose we count the positive integer lattice points beneath a convex decreasing curve in the first quadrant having equal intercepts. Then stretch in the coordinate directions so a…
Eigenvalue estimates on quantum graphs
Sinan Ariturk
On a finite connected metric graph, we establish upper bounds for the eigenvalues of the Laplacian. These bounds depend on the length, the Betti number, and the number of pendant v…
Maximal spectral surfaces of revolution converge to a catenoid
Sinan Ariturk
We consider a maximization problem for eigenvalues of the Laplace-Beltrami operator on surfaces of revolution in with two prescribed boundary components. For every $…
Pucci eigenvalues on geodesic balls
Sinan Ariturk
We study the eigenvalue problem for the Riemannian Pucci operator on geodesic balls. We establish upper and lower bounds for the principal Pucci eigenvalues depending on the curvat…
Simons' cone and equivariant maximization of the first -Laplace eigenvalue
Sinan Ariturk
We consider an optimization problem for the first Dirichlet eigenvalue of the -Laplacian on a hypersurface in , with . If , then among hype…
An annulus and a half-helicoid maximize Laplace eigenvalues
Sinan Ariturk
The Dirichlet eigenvalues of the Laplace-Beltrami operator are larger on an annulus than on any other surface of revolution in with the same boundary. This is establ…