arXiv research

Study on heat trace expansion for thermoelastic Dirichlet-to-Neumann map.

The paper studies magnetic field effects on surface eigenvalues and spectral properties.

Study reveals how to determine area and curvature from fluid flow resonances.

Researchers derive asymptotic expansions for thermoelastic operators on manifolds.

Study of Dirichlet minimizers on manifolds with boundary and their asymptotic behavior.

Paper develops formulas for shape derivatives in wave scattering.

The paper calculates spectral invariants of magnetic Steklov eigenvalues on Riemannian manifolds.

In this paper, the elastic Dirichlet-to-Neumann map $Ξ_g$ is studied for the stationary elasticity system in a compact Riemannian manifold $(Ω,g)$ with smooth boundary $\partial Ω$. By overcoming methodological difficulties, we explicitly get matrix-valued full symbol for the elastic Dirichlet-to-Neumann map $Ξ_g$. We …

Study on Yang-Mills equations on conformally compact manifolds, finding obstructions and asymptotics.

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$. This model provides an elementary description of the growth of a production economy in the long run. The system turns from a contracting to an expanding phase as $N$ in…

The paper solves the problem of fitting an ellipsoid to random points efficiently.

We establish an asymptotic relation between the spectrum of the discrete Laplacian associated to discretizations of a half-translation surface with a flat unitary vector bundle and the spectrum of the Friedrichs extension of the Laplacian with von Neumann boundary conditions. As an interesting byproduct of our study, w…

Study calculates geometric invariants from Navier-Lamé spectrum.

We show that in any harmonic space, the eigenvalue spectra of the Laplace operator on small geodesic spheres around a given point determine the norm $|\nabla R|$ of the covariant derivative of the Riemannian curvature tensor in that point. In particular, the spectra of small geodesic spheres in a harmonic space determi…

New upper bound for Neumann Laplacian eigenvalues on convex domains.

Sharp lower bound for first Neumann eigenvalue found in terms of diameter and width.

Study non-linear Dirichlet-to-Neumann map for Poincaré-Einstein fillings.

Study bounds the measure of zero sets of Neumann Laplace eigenfunctions.

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

The paper compares eigenvalues of Dirichlet, Neumann, and Laplacian on graphs.

Geodesic disks maximize the first non-trivial Neumann eigenvalue on spheres.

Algorithm transforms weakly negative plumbing trees to negative definite ones.

Sharp isoperimetric inequalities for Neumann eigenvalues in symmetric spaces.

Neumann's work connects 3-manifold invariants to quantum topology.

This paper is devoted to a proof of a generalized Ray-Singer conjecture for a manifold with boundary (the Dirichlet and the Neumann boundary conditions are independently given on each connected component of the boundary and the transmission boundary condition is given on the interior boundary). The Ray-Singer conjectur…

Recently, the first named author together with Xinan Ma \cite{ma2015neumann}, have proved the existence of the Neumann problems for Hessian equations. In this paper, we proceed further to study classical Neumann problems for Hessian equations. We prove here the existence of classical Neumann problems under the uniforml…

Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.

Study inverse boundary value problem for Monge-Ampère equation on convex domains.

Study solves a mathematical problem related to elliptic Schroedinger-to-Neumann maps.

Universal inequalities for Laplacian eigenvalues on convex domains.

Study on biharmonic Steklov problems with Neumann boundary conditions and eigenvalue estimates.

Study uniquely determines Riemannian metric derivatives from boundary data.

Two geodesic balls maximize the third Neumann eigenvalue in hyperbolic space.

New inequalities for planar convex domains' Laplacian eigenvalues.

Researchers calculate spectral invariants from Dirichlet-to-Neumann map for Witten-Laplacian with potential.

Study Neumann problem for special Lagrangian type equations.

Study relative commutants in von Neumann algebras using contraction notions.

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 compact Riemannian manifolds with boundary and a higher order generalization of the Dirichlet-to-Neumann map on graphs introduced by Hua-Huang-W…

Neumann eigenmaps improve landmark-based diffusion map embeddings.

Sharp inequality outside ball proved using Neumann method.

Solves Neumann problem on CR manifold boundary.

Study connects boundary geometry to symbol of Dirichlet-to-Neumann operator.

We study new heat kernel estimates for the Neumann heat kernel on a compact manifold with positive Ricci curvature and convex boundary. As a consequence, we obtain new lower bounds for the Neumann eigenvalues which are consistent with Weyl's asymptotics.

Paper derives formulas for static Einstein spaces, linking Neumann data to stability.

In this paper, we prove long time existence and convergence results for a class of general curvature flows with Neumann boundary condition. This is the first result for the Neumann boundary problem of non Monge-Ampere type curvature equations. Our method also works for the corresponding elliptic setting.

Abstract: Shows nonexistence of Courant-type nodal domain bounds for eigenfunctions of Dirichlet-to-Neumann operator.

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers minimize a cost function consisting of a data-fit term, which measures how well a…

It is shown that the Novikov inequalities for critical points of closed 1-forms hold with the von Neumann Betti numbers replacing the Novikov numbers. As a corollary we obtain a vanishing theorem for $L^2$ cohomology, generalizing a theorem of W. Lueck. We also prove that von Neumann Betti numbers coincide with the Nov…