Related papers: Robin and Steklov isospectral manifolds
This paper studies eigenvalues of some Steklov problems. Among other things, we show the following sharp estimtes. Let $\Omega$ be a bounded smooth domain in an $n(\geq 2)$-dimensional Hadamard manifold an let $0=\lambda_0 < \lambda_1\leq…
We study the first nonzero Steklov eigenvalue $\lambda_2(T,\delta\Omega)$ of the Dirichlet-to-Neumann operator on a finite tree $T$ with leaf boundary $\delta\Omega$, under a constraint on the diameter $D$. He and Hua [Calc. Var. PDE, 2022]…
We prove geometric upper bounds for the Poincar\'e and Logarithmic Sobolev constants for Brownian motion on manifolds with sticky reflecting boundary diffusion i.e. extended Wentzell-type boundary condition under general curvature…
We study the nodal set of the Steklov eigenfunctions on the boundary of a smooth bounded domain in $\mathbb{R}^n$ - the eigenfunctions of the Dirichlet-to-Neumann map. Under the assumption that the domain $\Omega$ is $C^2$, we prove a…
By calculating full symbol for the Dirichlet-to-Neumann map $\Lambda$ of a Stokes flow, we establish the asymptotic expansion of the trace of the heat kernel for $\Lambda$. We also give a useful procedure, by which all coefficients of the…
In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth…
The magnetic Dirichlet-to-Neumann map encodes the voltage-to-current measurements under the influence of a magnetic field. In the case of surfaces, we provide precise spectral asymptotics expansion (up to arbitrary polynomial power) for the…
We construct a sequence of boundary value problems on compact subsets of smooth noncompact hyperbolic surfaces of finite area. We prove that the sesquilinear forms associated to these boundary value problems are stable as well as consistent…
We construct the first non-trivial examples of compact non-isometric Alexandrov spaces which are isospectral with respect to the Laplacian and not isometric to Riemannian orbifolds. This construction generalizes independent earlier results…
We construct a Laplace isospectral deformation of metrics on an orbifold quotient of a nilmanifold. Each orbifold in the deformation contains singular points with order two isotropy. Isospectrality is obtained by modifying a generalization…
In this paper we construct compact manifolds with fixed boundary geometry which admit Riemannian metrics of unit volume with arbitrarily large Steklov spectral gap. We also study the effect of localized conformal deformations that fix the…
We give upper bounds for the Poincar\'e and Logarithmic Sobolev constants for doubly weighted Brownian motion on manifolds with sticky reflecting boundary diffusion under curvature assumptions on the manifold and its boundary. We therefor…
We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.
The Steklov problem on a compact Lipschitz domain is to find harmonic functions on the interior whose outward normal derivative on the boundary is some multiple (eigenvalue) of its trace on the boundary. These eigenvalues form the Steklov…
The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann spectrum, one orientable, the other…
We prove Reilly-type upper bounds for divergence-type operators of the second order as well as for Steklov problems on submanifolds of Riemannian manifolds of bounded sectional curvature endowed with a weighted measure.
Given a closed manifold $M$ and a closed connected submanifold $N\subset M$ of positive codimension, we study the Steklov spectrum of the domain $\Omega_\varepsilon\subset M$ obtained by removing the tubular neighbourhood of size…
In this paper, we study the Steklov eigenvalue of a Riemannian manifold (M, g) with smooth boundary. For compact M , we establish a Cheeger-type inequality for the first Steklov eigenvalue by the isocapacitary constant. For non-compact M ,…
We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2-spheres in simply connected 4-manifolds, which are topologically isotopic and whose complement has a prescribed fundamental group that satisfies some…
In this note, we find a sharp upper bound for the Steklov spectrum on a submanifold of revolution in Euclidean space with one boundary component.