arXiv research

Formula calculates index for CR operators on surfaces with boundary punctures.

The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.

Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.

Standardizes weighted ranking correlation coefficients to maintain zero expected value.

New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.

We revisit the question of existence and regularity of minimizers to weighted least gradient problems on a fixed bounded domain, subject to a Dirichlet boundary condition, in the case where the boundary data is continuous and the weight function is C^2 and bounded away from zero. Under suitable geometric conditions on …

Paper proposes approximate Stein classes for efficient truncated density estimation.

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

Adapts Stein's method for geometric inequalities, addressing boundary terms.

New metrics on 3D manifolds with large Steklov eigenvalues.

Given a compact four-dimensional Riemannian manifold $(M, g)$ with boundary, we study the problem of existence of Riemannian metrics on $M$ conformal to $g$ with prescribed $Q$-curvature in the interior $\mathring{M}$ of $M$, and zero $T$-curvature and mean curvature on the boundary $\partial M$ of $M$. This geometric …

Numerical methods solve Steklov eigenvalue problems to generate free boundary minimal surfaces.

The paper calculates area Siegel--Veech constants for specific submanifolds of REL zero.

We define two types of local indices of a vector field at an isolated zero on the boundary, and prove Poincare-Hopf-type index theorems for certain vector fields on a compact smooth manifold which have only isolated zeros.

Study Dirac operators on finite warped cylinders with gauge fields.

Paper proves surfaces with specific symmetries have the first Steklov eigenvalue.

ZeroS improves Transformers by adding negative weights, matching or beating softmax attention.

Upper bounds on constants for Brownian motion with sticky boundary.

We show that the complex hyperbolic metrics defined by Deligne-Mostow and Thurston on ${\mathcal{M}}_{0,n}$ are singular Kähler-Einstein metrics when ${\mathcal{M}}_{0,n}$ is embedded in the Deligne-Mumford-Knudsen compactification $\overline{\mathcal{M}}_{0,n}$. As a consequence, we obtain a formula computing the volu…

The paper finds large Steklov eigenvalues on manifolds using homogenization.

We study Riemannian manifolds with boundary under a lower $N$-weighted Ricci curvature bound for $N$ at most $1$, and under a lower weighted mean curvature bound for the boundary. We examine rigidity phenomena in such manifolds with boundary. We conclude a volume growth rigidity theorem for the metric neighborhoods of …

Study solves Yamabe problems on metric measure spaces with or without boundary.

Minimal surfaces in a ball have limited area.

We consider an elliptic self-adjoint first order differential operator L acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of the operator L is assumed to be trace-free and the subprincipal symbol is assumed to be zero. Gi…

We consider the tomography problem of recovering a covector field on a simple Riemannian manifold based on its weighted Doppler transformation over a family of curves $Γ$. This is a generalization of the attenuated Doppler transform. Uniqueness is proven for a generic set of weights and families of curves under a condi…

Let $M$ be a weighted manifold with boundary $\partial M$, i.e., a Riemannian manifold where a density function is used to weight the Riemannian Hausdorff measures. In this paper we compute the first and the second variational formulas of the interior weighted area for deformations by hypersurfaces with boundary in $\p…

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

We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition, and a suitable condition for the weighted mean curvature for the boundary, we ob…

Let (M,g) a compact Riemannian n-dimensional manifold with umbilic boundary. It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature hypersurface. In this paper we prove that these metrics are a compact set, provi…

Study compares manifolds with boundary under weighted Ricci curvature bounds.

The study examines stable regions in weighted manifolds with boundary properties.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

The study characterizes hypersurfaces in weighted cylinders and generalizes confinement properties.

Constructs minimal surfaces near the boundary of a ball.

The paper studies static manifolds with boundary and their properties.

Let $(M^n,g),~n\ge 3$ be a noncompact complete Riemannian manifold with compact boundary and $f$ a smooth function on $\partial M$. In this paper we show that for a large class of such manifolds, there exists a metric within the conformal class of $g$ that is complete, has zero scalar curvature on $M$ and has mean curv…

Online learning makes sequence of decisions with partial data arrival where next movement of data is unknown. In this paper, we have presented a new technique as multiple times weight updating that update the weight iteratively forsame instance. The proposed technique analyzed with popular state-of-art algorithms from …

Study classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.

Introduces electrostatic manifolds with boundary for curvature problems.

A new flow method solves the weighted Yamabe problem with boundary.

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

We study Kahler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold $K$ has $l\ge2$ boundary components (possibly $l=\infty$), then it has first betti number at least $l-1$, and the Levi form of any boundary component is zero. If $K…

Study on free boundary minimal hypersurfaces in Schwarzschild space, proving zero Morse index for certain hypersurfaces.

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

Let $M$ be a compact, connected Riemannian manifold whose Riemannian volume measure is denoted by $σ$. Let $f: M \rightarrow \mathbb{R}$ be a non-constant eigenfunction of the Laplacian. The random wave conjecture suggests that in certain situations, the value distribution of $f$ under $σ$ is approximately Gaussian. Wr…

In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to zero, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler …

The paper solves conditions for prescribing scalar and Gauss curvatures on manifolds with zero first eigenvalue.

Automates zero-shot classification by scoring and weighting prompts.