Some recent developments on the Steklov eigenvalue problem
The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of
interest in the past few decades. This article is a tour of some of the recent developments …
interest in the past few decades. This article is a tour of some of the recent developments …
The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript
How close is the Dirichlet-to-Neumann (DtN) map to the square root of the corresponding
boundary Laplacian? This question has been actively investigated in recent years …
boundary Laplacian? This question has been actively investigated in recent years …
A note on the magnetic Steklov operator on functions
T Chakradhar, K Gittins, G Habib… - arXiv preprint arXiv …, 2024 - arxiv.org
We consider the magnetic Steklov eigenvalue problem on compact Riemannian manifolds
with boundary for generic magnetic potentials and establish various results concerning the …
with boundary for generic magnetic potentials and establish various results concerning the …
Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds
MA Karpukhin - arXiv preprint arXiv:1512.09038, 2015 - arxiv.org
Consider a compact Riemannian manifold with boundary. In this short note we prove that
under certain positive curvature assumptions on the manifold and its boundary the Steklov …
under certain positive curvature assumptions on the manifold and its boundary the Steklov …
Dirichlet-to-Neumann maps for differential forms on graphs and their eigenvalues
Y Shi, C Yu - Journal of Mathematical Analysis and Applications, 2022 - Elsevier
In this paper, we first introduce Dirichlet-to-Neumann maps for differential forms on graphs
which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann …
which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann …
Higher order Dirichlet-to-Neumann maps on graphs and their eigenvalues
Y Shi, C Yu - arXiv preprint arXiv:1904.03880, 2019 - arxiv.org
In this paper, we first introduce higher order Dirichlet-to-Neumann maps on graphs which
can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on …
can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on …
Eigenvalue bounds for the Steklov problem on differential forms in warped product manifolds
T Chakradhar - arXiv preprint arXiv:2410.21138, 2024 - arxiv.org
We consider the Steklov problem on differential $ p $-forms defined by M. Karpukhin and
present geometric eigenvalue bounds in the setting of warped product manifolds in various …
present geometric eigenvalue bounds in the setting of warped product manifolds in various …
Decompositions of surface vector fields and topological characterizations of the codimensions
S Fukushima, H Kang - arXiv preprint arXiv:2311.14256, 2023 - arxiv.org
We prove that the space of vector fields on the boundary of a bounded domain in three
dimensions is decomposed into three subspaces orthogonal to each other: elements of the …
dimensions is decomposed into three subspaces orthogonal to each other: elements of the …
Steklov and Robin isospectral manifolds
C Gordon, P Herbrich, D Webb - Journal of Spectral Theory, 2021 - ems.press
We use two of the most fruitful methods for constructing isospectral manifolds, the Sunada
method and the torus action method, to construct manifolds whose Dirichlet-to-Neumann …
method and the torus action method, to construct manifolds whose Dirichlet-to-Neumann …
Robin and Steklov isospectral manifolds
C Gordon, P Herbrich, D Webb - arXiv preprint arXiv:1808.10741, 2018 - arxiv.org
We use two of the most fruitful methods for constructing isospectral manifolds, the Sunada
method and the torus action method, to construct manifolds whose Dirichlet-to-Neumann …
method and the torus action method, to construct manifolds whose Dirichlet-to-Neumann …