arXiv research

It is extended a result due to B. Guan and J. Spruck on the asymptotic Plateau's problem for CMC radial graphs in hyperbolic space to horizontal CMC graphs.

Study finds existence and uniqueness of CMC graphs in multiply connected domains.

The paper classifies CMC free boundary hypersurfaces in rotational domains.

The study examines graphs over domains in product manifolds, revealing properties of geodesics and constant curvature.

The paper proves the existence of CMC hypersurfaces in hyperbolic space.

The Dirichlet problem solved for CMC graphs in Sol_3.

The paper constructs complete CMC hypersurfaces in high-dimensional spaces.

The study finds conditions for CMC surfaces in a specific space with boundary in parallel planes.

It is proved that the holomorphic quadratic differential associated to CMC surfaces in Riemannian products $\mathbb{S}^2\times\Rr$ and $\mathbb{H}^2\times \Rr$ discovered by U. Abresch and H. Rosenberg could be obtained as a linear combination of usual Hopf differentials. Using this fact, we are able to extend it for L…

Survey on rigidity results for graphs with prescribed mean curvature.

The paper extends CMC surface theory to product spaces, proving height estimates and classifying surfaces.

CMC-1 surfaces linked via Möbius transformations between circle patterns.

Paper proves a theorem about constant mean curvature surfaces in isotropic 3-space.

Paper generalizes discrete CMC surfaces and shows how they can be derived.

New method improves curvature estimates for stable surfaces.

This is a survey on the global theory of constant mean curvature surfaces in Riemannian homogeneous 3-manifolds. These ambient 3-manifolds include the eight canonical Thurston 3-dimensional geometries, i.e. R3, H3, S3, H2 \times R, S2 \times R, the Heisenberg space Nil3, the universal cover of PSL2(R) and the Lie group…

Researchers prove constant mean curvature graphs in hyperbolic 3-space for specific domains.

Study on stable CMC surfaces in slabs with boundary conditions.

This thesis constructs cmc 1/2 surfaces from catenoids, proving convergence and solving boundary value problems.

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…

The paper constructs unstable and outlying CMC spheres in specific manifolds.

The paper studies stable surfaces in sub-Riemannian 3-space forms.

New CMC surfaces with dihedral symmetry constructed from Darboux transforms.

No proper biharmonic CMC compact hypersurface in a specific warped product space.

We propose an extension of the structure equation for constant mean curvature (CMC) surfaces in a three dimensional Riemannian space form to the associated CMC hierarchy of evolution equations by the higher-order commuting symmetries. Via the canonical formal Killing field, considered as an infinitely prolonged and loo…

We study constant mean curvature graphs in the Riemannian 3-dimensional Heisenberg spaces ${\cal H}={\cal H}(τ)$. Each such ${\cal H}$ is the total space of a Riemannian submersion onto the Euclidean plane $\mathbb{R}^2$ with geodesic fibers the orbits of a Killing field. We prove the existence and uniqueness of CMC gr…

Proves non-vanishing CMC flux for specific manifolds.

Constructs cmc doublings of minimal surfaces via min-max theory.

We translate a classification scheme for periodic CMC surfaces developed by J. Dorfmeister and the author to discrete CMC surfaces in the sense of A. Bobenko and U. Pinkall. The scheme uses the dressing action on discrete CMC surfaces to arrive at a classification for periodic discrete CMC surfaces.

Compactness proven for CMC surfaces with bounded topology and boundary length.

Proves special foliation property of SS-CMC hypersurfaces in Schwarzschild spacetime.

We will discuss some sharp estimates for CMC graphs in a Riemannian 3-manifold MxR whose boundary is contained in a slice. We will start by giving sharp lower bounds for the geodesic curvature of the boundary and improve these bounds when assuming additional restrictions on the maximum height that such a surface reache…

New cosmological spacetimes without CMC Cauchy surfaces found.

Unique CMC foliation in Minkowski space solved.

Study singularities of CMC 1 surfaces in de Sitter space.

Survey on CMC surfaces in homogeneous 3-manifolds.

Proves existence and uniqueness of CMC foliations in cuspidal manifolds.

Estimates bandwidth for CMC initial data sets.

Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces established.

The paper explores CMC hypersurfaces in spheres, verifying Yau's conjecture.

Authors review CMC spacelike hypersurfaces and new existence results.

Study finds existence and non-existence of large stable CMC spheres in asymptotically flat 3-manifolds.

New CMC existence result for expanding cosmological spacetimes.

Python tool for constructing CMC surfaces using DPW method.

In this paper we numerically construct CMC deformations of the Lawson minimal surfaces $ξ_{g,1}$ using a spectral curve and a DPW approach to CMC surfaces in spaceforms.

Study of CMC spheres in Heisenberg group, proving conjecture.

Study on proper-biharmonic flat tori in spheres with CMC conditions.

The study constructs free boundary CMC annuli in spherical and hyperbolic balls.