arXiv research

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

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…

Study uniquely determines Riemannian metric derivatives from boundary data.

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

Neumann eigenmaps improve landmark-based diffusion map embeddings.

Paper generalizes kernel mean embedding to von Neumann-algebra-valued measures.

We study mean curvature flow of smooth, axially symmetric surfaces in $\mathbb{R}^3$ with Neumann boundary data. We show that all singularities at the first singular time must be of type I.

Twisted Neumann--Zagier matrices for quantum invariants.

Method learns Dirichlet-to-Neumann maps on graphs using Gaussian processes.

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.

ASTRA improves TDA by more accurately approximating iHVP.

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

We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametrized family of limit energy measures is Brakke's mean curvature flow with a generalized right angle condition on the boundary.

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

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

Stokes equations help uniquely identify manifold metrics from boundary data.

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.

In this paper, we can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold $M^{n}\times\mathbb{R}$, where $M^{n}$ is an $n$-dimensional ($n\geq2$) complete Riemannian manifold with nonnegative Ricci curvature, and $\mat…

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

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.

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

Anisotropic metric on manifolds uniquely determined by boundary data.

New inequalities for planar convex domains' Laplacian eigenvalues.

We study the learnability of a class of compact operators known as Schatten--von Neumann operators. These operators between infinite-dimensional function spaces play a central role in a variety of applications in learning theory and inverse problems. We address the question of sample complexity of learning Schatten-von…

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…

Sharp inequality outside ball proved using Neumann method.

Solves Neumann problem on CR manifold boundary.

New algorithms for clustering and dimension reduction using relative von Neumann entropy.

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.

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.

Study determines a minimal surface in a Riemannian manifold from boundary data.

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

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…

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…