arXiv research

Study uniquely determines Riemannian metric derivatives from boundary data.

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

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

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

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.

The paper classifies solutions to a Liouville equation on a half-space with a specific boundary condition.

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 …

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

The paper finds a family of 2D surfaces where Laplacian and Dirichlet-to-Neumann commute.

Sharp inequality outside ball proved using Neumann method.

The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

Quantitative Sobolev extensions lead to Neumann heat kernel bounds.

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

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

Abstract: Expresses zeta-determinant of Dirichlet-to-Neumann operator on forms.

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.

We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between…

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

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 Neumann problem for special Lagrangian type equations.

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

Study proves mean curvature flow in GRW spacetimes with perpendicular boundary condition.

Recent research connects Hörmander's old work to modern boundary Laplacian analysis.

In this note, we study the prescribed mean curvature equation with Neumann boundary conditions on Riemannian product manifold $M^n\times \mathbb{R}$. The main goal is to establish the boundary gradient estimates for solutions by the maximum principle. As a consequence, we obtain an existence result.

Let $Ω$ be an open, bounded domain in the plane with connected and smooth boundary, and $ω$ an eigenfunction of the Neumann Laplacian corresponding to some Neumann eigenvalue $μ> 0$. If the boundary value of $ω$ is a nonzero constant along the boundary, denoting $0 = μ_1(Ω) < μ_2(Ω) <= ...$ the set of all Neumann eigen…

Stokes equations help uniquely identify manifold metrics from boundary data.

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

We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and existence results.

In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of biharmonic Stekloff eigenvalues with Neumann boundary condition in a bounded domain of an $n$-dimensional Riemannian manifold.

This paper demonstrates existence for all time of mean curvature flow in Minkowski space with a perpendicular Neumann boundary condition, where the boundary manifold is a convex cone and the flowing manifold is initially spacelike. Using a blowdown argument, we show that under renormalisation this flow converges toward…

Study sharp lower bounds on negative eigenvalues of magnetic Pauli operator.

Paper derives a formula for the determinant of Dirichlet-to-Neumann operator on Riemann surfaces.

In this paper, we mainly study eigenvalue problems of p-Laplacian on domains with an interior hole. Firstly we prove Faber-Krahn-type inequalities, and Cheng-type eigenvalue comparison theorems on manifolds. Secondly, we prove a comparison theorem for eigenvalues with inner Dirichlet and outer Neumann boundary in minim…

Anisotropic metric on manifolds uniquely determined by boundary data.

This paper shows that the time $t$ map of the averaged Euler equations, with Dirichlet, Neumann, and mixed boundary conditions is canonical relative to a Lie-Poisson bracket constructed via a non-smooth reduction for the corresponding diffeomorphism groups. It is also shown that the geodesic spray for Neumann and mixed…

Neumann eigenmaps improve landmark-based diffusion map embeddings.

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.

We consider strictly convex hypersurfaces which are evolving by the non-parametric logarithmic Gauss curvature flow subject to a Neumann boundary condition. Solutions are shown to converge smoothly to hypersurfaces moving by translation. In particular, for bounded domains we prove that convex functions with prescribed …

Wave equation map reveals manifold's structure.

We adapt the results of Part 1 to include the unit ball in the Heisenberg group, the model domain with characteristic boundary points. In particular, we construct function spaces on which the Kohn Laplacian with the \bar{\partial}_b-Neumann boundary conditions is an isomorphism. As an application, we establish sharp re…

BEKAN uses RBFs and evolutionary methods to solve PDEs with boundary conditions.

New equations reveal viscosity from boundary measurements.

In this work, we prove the existence of a family of solutions of the Allen-Cahn equation with nonlinear Neumann boundary condition under some constraints, whose nodal sets concentrate asymptotically to a given volume nondegenerate capillary hypersurface in a compact Riemannian manifold. Our construction is inspired by …

We establish sharp regularity and Fredholm theorems for the \bar{\partial}_b-Neumann problem on domains satisfying some non-generic geometric conditions. We use these domains to construct explicit examples of bad behaviour of the Kohn Laplacian: it is not always hypoelliptic up to the boundary, its partial inverse is n…

Study Dirichlet-to-Neumann maps on manifolds, focusing on covering and total spaces.

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…

Compactness proven for manifolds with nonnegative Ricci curvature and uniformly convex boundary.

Study Cheeger inequalities for Riemannian manifolds with boundary.