arXiv research

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

Study on nonlinear equations on spheres and hemispheres with zero Neumann boundary condition.

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

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 Sturm-Liouville problems with zero potential and Neumann boundary conditions.

Solves Neumann problem on CR manifold boundary.

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

We consider $n$-dimensional hypersurfaces flowing by mean curvature flow with Neumann free boundary conditions supported on a smooth support surface. We show that the Hausdorff $n$-measure of the singular set is zero. In fact, we consider two types of interaction between the support and flowing surfaces. In the case of…

Paper solves curvature prescription problem on surfaces with boundary.

In this paper we prove that, given a compact four dimensional smooth Riemannian manifold (M,g) with smooth boundary there exists a metric conformal to g with constant T-curvature, zero Q-curvature and zero mean curvature under generic and conformally invariant assumptions. The problem amounts to solving a fourth order …

Study uniquely determines Riemannian metric derivatives from boundary data.

Extends unique continuation theorem to manifolds with boundary, proving zero set codimension.

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

Let $Ω$ be a pseudoconvex domain with $C^2$-smooth boundary in $\mathbb CP^n$. We prove that the $\bar\partial-Neumann operator$N$exists for$(p,q)$-forms on$Ω$. Furthermore, there exists a$t_0>0$such that the operators$N$,$\bar\partial^*N$,$\bar\partial N$ and the Bergman projection are regular in the Sobolev …

We define the notion of an exceptional manifold to be a flat Riemannian manifold with boundary which supports a positive harmonic function satisfying simultaneously a zero Dirichlet condition and a constant (nonzero) Neumann condtion at the boundary. We study the two-dimensional case: we present various examples and gi…

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.

Study on axially symmetric surfaces' flow, showing all singularities are of type I.

Gradient Descent Ascent converges to von-Neumann solution in hidden zero-sum games.

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

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 …

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 constructs free boundary minimal surfaces in product spaces using eigenvalue methods.

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.

On a compact manifold $M^{n}$ ($n\geq 3$) with boundary, we study the asymptotic behavior as $ε$ tends to zero of solutions $u_ε: M \to \mathbb{C}$ to the equation $Δu_ε + ε^{-2}(1 - |u_ε|^{2})u_ε = 0$ with the boundary condition $\partial_νu_ε = 0$ on $\partial M$. Assuming an energy upper bound on the solutions and a…

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.

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.

Paper proves rigidity of weak solutions for anisotropic N-Laplacian equations with Neumann or Robin boundary conditions.

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.

The study finds lower bounds for the first eigenvalue of the Laplacian in planar domains with magnetic fields.

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.

Paper proves translating solutions for a specific flow in a product manifold.

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.

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…