arXiv research

New minimal surfaces found in ball with boundary constraints.

Study constructs disks with curved boundaries in a 3D ball.

Researchers determine the Thurston unit ball for a family of $n$-chained links and find conditions for fibered faces.

Let Σbe a k-dimensional minimal surface in the unit ball B^n which meets the unit sphere orthogonally. We show that the area of Σis bounded from below by the volume of the unit ball in R^k. This answers a question posed by R. Schoen.

Study inverse curvature flows for capillary hypersurfaces in a unit ball.

Two minimal hypersurfaces in a ball intersect in any half-ball.

The unit ball is characterized by a Kähler-Einstein potential.

Volume of unit balls defined by quadratic differentials is not proper and has integrable volume.

The paper proves new inequalities on the unit ball in higher dimensions.

Sharp upper bound for minimal graph area in unit ball established.

Article provides polytopes as dual unit balls of Thurston norms on 3-manifolds.

Using the flow method, we prove some existence results for the problem of prescribing the mean curvature on the unit ball. More precisely, we prove that there exists a conformal metric on the unit ball such that its mean curvature is $f$, when $f$ possesses certain reflection or rotation symmetry.

Study finds a minimal surface in a ball with specific properties.

Minimal normal curvature immersions in the unit ball studied.

Minimal surfaces in a ball have limited area.

Proves rigidity of maps between balls with Hölder boundary continuity.

In this paper, we construct an asymptotically hyperbolic metric with scalar curvature -6 on unit ball $\mathbf{D}^3$, which contains multiple horizons.

The paper characterizes unit balls among Stein spaces with specific groups using Bergman-Einstein metrics.

Geometric structures on quaternionic unit ball for slice regular Möbius transformations.

The purpose of the present paper is to show that the components of the unit normal of any minimal surface with free boundary in the unit ball, are eigenfunctions associated with the eigenvalue $-2$, for some (new) natural eigenvalue problem for the Jacobi operator; this fact has analytic (spectral) consequences for fre…

In this article we prove first of all the nonexistence of holomorphic submersions other than covering maps between compact quotients of complex unit balls, with a proof that works equally well in a more general equivariant setting. For a non-equidimensional surjective holomorphic map between compact ball quotients, our…

Sharp inequalities in unit ball with constraints on moments.

Constructs minimal surfaces in a 3-ball using PDE gluing.

Study of Riemannian geometry on quaternionic unit ball linked to Sp(1,1) group.

No radial balanced metrics found on Kepler manifold unit ball with mild boundary conditions.

Given a closed complex hypersurface $Z\subset \mathbb{C}^{N+1}$ $(N\in\mathbb{N})$ and a compact subset $K\subset Z$, we prove the existence of a pseudoconvex Runge domain $D$ in $Z$ such that $K\subset D$ and there is a complete proper holomorphic embedding from $D$ into the unit ball of $\mathbb{C}^{N+1}$. For $N=1$,…

New examples show non-rotational annuli in a ball, solving a uniqueness problem.

Proves spheres with bounded curvatures must contain a unit ball.

Two-dimensional domains with Kähler-Einstein Bergman metrics are biholomorphic to the unit ball.

The paper proves inequalities for hypersurfaces in a unit ball with specific boundary conditions.

In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the automorphism group and the regularity of the boundary.

Authors create stable proper biharmonic maps from unit ball to spheres.

Study minimal networks on spheres and balls near standard metrics.

If (M^n, g) is a complete Riemannian manifold with filling radius at least R, then we prove that it contains a ball of radius R and volume at least c(n)R^n. If (M^n, hyp) is a closed hyperbolic manifold and if g is another metric on M with volume at most c(n)Volume(M,hyp), then we prove that the universal cover of (M,g…

For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are completely described by combinatorial properties of the graph. We study then th…

Constructs a unique surface in a ball with specific properties.

Study on Santaló point for convex bodies in normed spaces.

New minimal annuli found in unit ball, solving old problems.

Study on curvature flow in 4D ball, proving existence and convergence.

The article studies mapping properties of Radon transform and backprojection on a unit ball.

In this article, we show that the critical catenoid, as a free boundary minimal surface of the unit ball in $\mathbb{R}^3$, has index $4$. We also prove that a free boundary minimal surface of the unit ball in $\mathbb{R}^3$, that is not a flat disk, has index at least $4$.

Motivated by a recent work of Ache and Chang concerning the sharp Sobolev trace inequality and Lebedev-Milin inequalities of order four on the Euclidean unit ball, we derive such inequalities on the Euclidean unit ball for higher order derivatives. By using, among other things, the scattering theory on hyperbolic space…

Let (M,g) be a simply connected complete Kahler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in C^n, where dim M = n.

Constructs minimal surfaces near the boundary of a ball.

Paper proves rigidity and index of Y-cones in unit ball.

A unique Kähler potential on the unit ball is identified with constant differential norm.

Study on exact Lagrangian submanifolds in unit ball with Legendrian boundary.

Study proves all free boundary CMC annuli are of finite type.