17 citations · 49 across the 15 of their papers we have counts for
17 papers
Ground states of semilinear elliptic equations
Rayssa Caju, Pedro Gaspar, Marco A. M. Guaraco +1
We study solutions of , where the potential can have an arbitrary number of wells at arbitrary heights, including bottomless wells with subcritical decay. In our…
A remark on the rigidity of the first conformal Steklov eigenvalue
Henrik Matthiesen, Romain Petrides
We show rigidity of the first conformal Steklov eigenvalue on annuli and Möbius bands. The proof relies, among others, on uniqueness results due to Fraser--Schoen, a compactness th…
Free boundary minimal surfaces of any topological type in Euclidean balls via shape optimization
Henrik Matthiesen, Romain Petrides
For any compact surface with smooth, non-empty boundary, we construct a free boundary minimal immersion into a Euclidean Ball where is controlled in terms of…
Handle attachment and the normalized first eigenvalue
Henrik Matthiesen, Anna Siffert
We show that the first eigenvalue of a closed Riemannian surface normalized by the area can be strictly increased by attaching a cylinder or a cross cap. As a consequence we obtain…
Sharp asymptotics of the first eigenvalue on some degenerating surfaces
Henrik Matthiesen, Anna Siffert
We study sharp asymptotics of the first eigenvalue on Riemannian surfaces obtained from a fixed Riemannian surface by attaching a collapsing flat handle or cross cap to it. Through…
The systole of large genus minimal surfaces in positive Ricci curvature
Henrik Matthiesen, Anna Siffert
We use Colding--Minicozzi lamination theory to study the systole of large genus minimal surfaces in an ambient three-manifold of positive Ricci curvature.
Bottom of spectra and amenability of coverings
Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis
For a Riemannian covering , the bottoms of the spectra of and coincide if the covering is amenable. The converse implication does not always hold. A…
Monotonicity results for the first Steklov eigenvalue on compact surfaces
Henrik Matthiesen, Romain Petrides
We show several results comparing sharp eigenvalue bounds for the first Steklov eigenvalue on surfaces under change of the topology. Among others, we obtain strict monotonicity in…
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…
Existence of metrics maximizing the first eigenvalue on non-orientable surfaces
Henrik Matthiesen, Anna Siffert
We prove the existence of metrics maximizing the first eigenvalue normalized by area on closed, non-orientable surfaces assuming two spectral gap conditions. These spectral gap con…
On the bottom of spectra under coverings
Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis
For a Riemannian covering of complete Riemannian manifolds with boundary (possibly empty) and respective fundamental groups , we show that the bottoms…
Extremal metrics for Laplace eigenvalues in perturbed conformal classes on products
Henrik Matthiesen
In this short note, we prove that conformal classes which are small perturbations of a product conformal class on a product with a standard sphere admit a metric extremal for some…
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…
Extremal metrics for Laplace eigenvalues in perturbed conformal classes
Henrik Matthiesen
We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a…
A regularity result for conformal metrics with large first eigenvalue and integral scalar curvature bounds
Henrik Matthiesen
We prove a regularity result for unit volume conformal metrics with integral scalar curvature bounds for and first eigenvalue of bounded from below by a constant $B > Λ…
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.