arXiv research

Paper classifies critical points in half-space with new distance function.

New theorem for nonlocal minimal surfaces in any dimension.

Paper studies stability of curved surfaces in a half-space.

Paper proves flatness of anisotropic minimal graphs in half-spaces.

We propose a simple proof of the vertical half-space theorem for Heisenberg space.

Anisotropic minimal graphs over half-spaces are flat.

For $n\geq2,$ we obtain Liouville type theorems for minimal surface equations in half space $\mathbf R^n_+$ with affine Dirichlet boundary value or constant Neumann boundary value.

Paper extends Wente's result to anisotropic capillary surfaces in half-spaces.

Study proves no minimal surfaces can be contained in certain half-spaces or cones.

A 3D catenoid in 4D space is a minimal hypersurface that cannot be extended to a higher-dimensional half-space.

Proves quantitative Alexandrov theorem for capillary surfaces.

The paper explores properties of 1-surfaces in hyperbolic space and proves strong half-space theorems.

The study proves properties of capillary graphs in half-spaces.

Study proves Liouville theorem for specific curvature equations with boundary conditions.

The study proves that certain minimal hypersurfaces in 4D space must be planes.

Develops theory for stable capillary minimal hypersurfaces in half-space.

We prove a half-space theorem for an ideal Scherk graph $Σ\subset M\times\mathbb R$ over a polygonal domain $D\subset M,$ where $M$ is a Hadamard surface whose curvature is bounded above by a negative constant. More precisely, we show that a properly immersed minimal surface contained in $D\times\mathbb R$ and disjoint…

We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a comparison principle with geometric barriers for establishing mean curvature estimates fo…

We study the embedded Calabi-Yau problem for complete embedded constant mean curvature surfaces of finite topology or of positive injectivity radius in a simply-connected three-dimensional Lie group X endowed with a left-invariant Riemannian metric. We first prove a half-space theorem for constant mean curvature surfac…

We study a half-space problem related to graphs in $\mathbb{H}^2\times\mathbb{R}$, where $\mathbb{H}^2$ is the hyperbolic plane, having constant mean curvature $H$ defined over unbounded domains in $\mathbb{H}^2$.

The study proves theorems about minimal and H-surfaces in 3D space.

This study proves the Half Space Property for RCD(0,N) and RCD(K,N) spaces.

Study classifies solutions to specific equations on half-space and ball.

Motivated by the large ammount of results obtained for minimal and positive constant mean curvature surfaces in several ambient spaces, the aim of this paper is to obtain half-space theorems for properly immersed surfaces in $\mathbb{R}^3$ whose mean curvature is given as a prescribed function of its Gauss map. In orde…

We prove some half-space theorems for minimal surfaces in the Heisenberg group Nil_3 and the Lie group Sol_3 endowed with their left-invariant Riemannian metrics. If S is a properly immersed minimal surface in Nil_3 that lies on one side of some entire minimal graph G, then S is the image of G by a vertical translation…

Paper extends capillary convex body results to anisotropic setting with Alexandrov-Fenchel inequalities.

Paper proves inequality for capillary hypersurfaces with new proof.

The paper proves nonexistence results for translating solitons in r-mean curvature flow.

The paper defines capacities for minimal graphs over manifolds and proves the half-space property.

In this paper, we prove a half-space theorem with respect to constant mean curvature $1/2$ entire graphs in $\mathbb{E(-1,τ)}$. If $Σ$ is such an entire graph and $Σ'$ is a properly immersed constant mean curvature $1/2$ surface included in the mean convex side of $Σ$ then $Σ'$ is a vertical translate of $Σ$. We also h…

Study proves rigidity of critical points in hydrophobic capillary systems.

We construct a one-parameter family of properly embedded minimal annuli in the Heisenberg group Nil_3 endowed with a left-invariant Riemannian metric. These annuli are not rotationally invariant. This family gives a vertical half-space theorem and proves that each complete minimal graph in Nil_3 is entire. Also, the si…

The paper applies a capillary John ellipsoid theorem to solve capillary curvature problems.

Using the Fourier analysis techniques on hyperbolic spaces and Green's function estimates, we confirm in this paper the conjecture given by the same authors in [43]. Namely, we prove that the sharp constant in the $\frac{n-1}{2}$-th order Hardy-Sobolev-Maz'ya inequality in the upper half space of dimension $n$ coincide…

Minimal graph theorem proven for convex domains.

Developed a half-space model for pseudo-hyperbolic space.

Study extends eigenvalue formulas to weighted manifolds and proves global rigidity theorems.

Paper introduces capillary Schwarz symmetrization in half-space.

The paper establishes inequalities for $p$-capacitary functions in flat half-spaces.

The article constructs helicoidal and catenoidal minimal surfaces in a Lie group.

The study characterizes convex bodies with equal isoperimetric profiles to half-spaces and estimates their volume behavior.

Study on minimal surfaces with free boundary in a half-space, improving index estimates.

Paper solves inequalities for capillary hypersurfaces in half-spaces.

New Minkowski inequality for capillary surfaces in half-space.

Proposes NUV priors for half-space and box constraints.

Paper analyzes iterative learning for concept classes and learns half-spaces.

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

The paper proves inequalities for convex capillary hypersurfaces in a half-space.