arXiv research

We study integrable geodesic flows on Stiefel varieties $V_{n,r}=SO(n)/SO(n-r)$ given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics. We also consider natural generalizations of the Neumann systems on $V_{n,r}$ with the above metrics and proves their integrability in the non-commutative sense b…

We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to…

Study applies inverse scattering to BKM systems, linking spectra and integrable systems.

Generalizes results on Bieri-Neumann-Strebel-Renz invariants and tropical varieties.

Study on smoothness of solutions to nonlinear equations on Riemannian manifolds.

Describes geodesic scattering on hyperboloids using quadrics results.

New equations reveal viscosity from boundary measurements.

Abstract: Determines thermoelastic coefficients from boundary data.

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 …

Using the functional associated with the optimal Wente inequality for pairs of functions on 2-dimensional domains, we show the existence of solutions to the H-system on an annulus satisfying Neumann boundary conditions.

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.

The paper explores rigidity and proximality in dynamical systems, proving new results about $C^*$-algebras.

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…

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 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.

BNSR invariants are contained in the complement of tropical varieties.

In this work, we develop a study involving some nonlinear partial differential equations on spheres and hemispheres, with the zero Neumann boundary condition, which are so-called Brezis-Nirenberg type problems, and we give conditions on which such equations have only constant solutions. We also extend these results for…

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.

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

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…

Twisted Neumann--Zagier matrices for quantum invariants.