arXiv research

Study series invariants of plumbed 3-manifolds using root lattices.

ASTRA improves TDA by more accurately approximating iHVP.

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…

This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional time-homogeneous diffusions even for the cases where the corresponding transition den…

Study reveals how boundary wave operator determines metric properties on anti-de Sitter spacetimes.

Dirichlet-Neumann duality for Riemannian submersions

In this paper, we revisit the recurrent back-propagation (RBP) algorithm, discuss the conditions under which it applies as well as how to satisfy them in deep neural networks. We show that RBP can be unstable and propose two variants based on conjugate gradient on the normal equations (CG-RBP) and Neumann series (Neuma…

The paper shows connections can be uniquely determined by their boundary data.

We continue the study of the operator of generalized Maxwell equations and completely discover the behavior of the solutions of the time-harmonic equations as the frequency tends to zero. Thereby, we identify degenerate operators in terms of special 'polynomially growing' solutions of a corresponding static problem, wh…

We give a formula for the radial asymptotics to all orders of the special $q$-hypergeometric series known as Nahm sums at complex roots of unity. This result is used in~\cite{CGZ} to prove one direction of Nahm's conjecture relating the modularity of Nahm sums to the vanishing of a certain invariant in $K$-theory. The …

New upper bound for Neumann Laplacian eigenvalues on convex domains.

The Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of th…

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.

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.

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.

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…

We investigate the formation of singularities for surfaces evolving by volume preserving mean curvature flow. For axially symmetric flows - surfaces of revolution - in $\mathbb{R}^3$ with Neumann boundary conditions, we prove that the first developing singularity is of Type I. The result is obtained without any additio…

Twisted Neumann--Zagier matrices for quantum invariants.

Study proves inequalities for eigenvalues of symmetric domains in space forms.

In this paper, we consider the global regularity for Monge-Ampère type equations with the Neumann boundary conditions on Riemannian manifolds. It is known that the classical solvability of the Neumann boundary value problem is obtained under some necessary assumptions. Our main result extends the main theorem from the …