24 citations · 50 across the 16 of their papers we have counts for
16 papers
Small eigenvalues of pseudo-Laplacians
Werner Ballmann, Sugata Mondal, Panagiotis Polymerakis
We extend the Otal-Rosas bound on the number of small eigenvalues of the Laplacian on a hyperbolic surface to the small eigenvalues of pseudo-Laplacians. In the process, we extend…
On the spectral stability of finite coverings
Werner Ballmann, Sugata Mondal, Panagiotis Polymerakis
We prove the non-existence of new eigenvalues in for specific and random finite coverings of a complete and connected Riemannian manifold with Ricci curvature bounded f…
Spectral instability of coverings
Sugata Mondal, Werner Ballmann
We study the behaviour of eigenvalues, below the bottom of the essential spectrum, of the Laplacian under finite Riemannian coverings of complete and connected Riemannian manifolds…
Some remarks on critical sets of Laplace eigenfunctions
Chris Judge, Sugata Mondal
We study the set of critical points of a solution to and in particular components of the critical set that have codimension 1. We show, for example, that if a secon…
Critical points of Laplace eigenfunctions on polygons
Chris Judge, Sugata Mondal
We study the critical points of Laplace eigenfunctions on polygonal domains with a focus on the second Neumann eigenfunction. We show that if each convex quadrilaterals has no seco…
Euclidean Triangles Have No Hot Spots
Chris Judge, Sugata Mondal
We show that a second Neumann eigenfunction u of a Euclidean triangle has no critical points in the interior of the triangle.
Small eigenvalues of surfaces - old and new
Werner Ballmann, Henrik Matthiesen, Sugata Mondal
We discuss our recent work on small eigenvalues of surfaces. As an introduction, we present and extend some of the by now classical work of Buser and Randol and explain novel ideas…
An arithmetic property of the set of angles between closed geodesics on hyperbolic surfaces of finite type
Sugata Mondal
For a hyperbolic surface S of finite type we consider the set A(S) of angles between closed geodesics on S. Our main result is that there are only finitely many rational multiples…
Rigidity of length-angle spectrum for closed hyperbolic surfaces
Sugata Mondal
The rigidity of marked length spectrum for closed hyperbolic surfaces due to Fricke-Klein [7] has been the motivation of many different rigidity results, specially for manifolds of…
On the analytic systole of Riemannian surfaces of finite type
Werner Ballmann, Henrik Matthiesen, Sugata Mondal
In our previous work we introduced, for a Riemannian surface , the quantity , where denotes the first Dirichlet eigenvalue of and the infimum i…
Geodesics and nodal sets of Laplace eigenfunctions on hyperbolic manifolds
Chris Judge, Sugata Mondal
Let X be a manifold equipped with a complete Riemannian metric of constant negative curvature and finite volume. We demonstrate the finiteness of the collection of totally geodesic…
Small eigenvalues of surfaces of finite type
Sugata Mondal, Werner Ballmann, Henrik Matthiesen
Extending our previous work on eigenvalues of closed surfaces and work of Otal and Rosas, we show that a complete Riemannian surface S of finite type and negative Euler characteris…
Small eigenvalues of surfaces
Werner Ballmann, Henrik Matthiesen, Sugata Mondal
We show that the Laplacian of a Riemannian metric on a closed surface S with Euler characteristic χ(S) < 0 has at most -χ(S) small eigenvalues.
On topological upper-bounds on the number of small cuspidal eigenvalues
Sugata Mondal
Let be a noncompact, finite area hyperbolic surface of type . Let denote the Laplace operator on . As varies over the {\it moduli space} ${\mathcal{M}_{g,…
On largeness and multiplicity of the first eigenvalue of hyperbolic surfaces
Sugata Mondal
We apply topological methods to study the smallest non-zero number in the spectrum of the Laplacian on finite area hyperbolic surfaces. For closed hyperbolic surfaces of genu…
Systole and of a hyperbolic surface
Sugata Mondal
We apply topological methods to study eigenvalues of the Laplacian on closed hyperbolic surfaces. For any closed hyperbolic surface of genus , we get a geometric lower bound…