arXiv research

3-balls in 4-sphere become isotopic in 5-ball.

Study on ball widths and minimal submanifolds in space forms.

This paper describes a method to construct standard 4-balls from homotopy 4-balls in $\mathbb{C}^2$.

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

New surface area measures defined for ball-convex bodies, leading to entropy and inequalities.

Sharp lower bound found for geodesic ball eigenvalues.

Paper calculates ball number of links using Lorentz geometry and circle packing.

Quantifies nearly spherical subsets in complex ball geometry.

Sharp geometric inequalities for free boundary hypersurfaces in balls.

New minimal surfaces found in ball with boundary constraints.

New examples show non-locally-flat PL-disk bounds in rational homology balls but not in integer homology balls.

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

Study shows no smooth embeddings of rational homology balls into complex projective plane.

Sharp inequality outside ball proved using Neumann method.

Fourth-order problem on half-ball with corner behavior.

Classifies surgeries on torus knots and cables that bound rational homology balls.

New illumination bodies defined for ball-convex shapes, proving convexity and establishing surface area measures.

In hyperbolic space $H^n$ we set a geodesic ball of radius $ρ$. Consider a $k$ dimensional minimal submanifold passing through the origin of the geodesic ball with boundary lies on the boundary of that geodesic ball. We prove that its area is no less than the totally geodesic $k$ dimensional submanifold passing through…

Study non-existence of complex ball quotients in Torelli locus.

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

Fintushel and Stern showed that the Brieskorn sphere $Σ(2,3,7)$ bounds a rational homology ball, while its non-trivial Rokhlin invariant obstructs it from bounding an integral homology ball. It is known that their argument can be modified to show that the figure-eight knot is rationally slice, and we use this fact to p…

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

Sharp inequality found on three-balls for fourth order Sobolev traces.

Study shows Seifert fibered spaces don't bound rational homology balls.

New balls smoothly fit in CP² but not symplectically.

We prove the diameter of the intersection of two closed convex balls in a Riemannian manifold eventually decreases continuously as the centers of the balls move apart.

We describe two methods for showing that a vector can not be the f-vector of a homology d-ball. As a consequence, we disprove a conjectured characterization of the f-vectors of balls of dimension five and higher due to Billera and Lee. We also provide a construction of triangulated balls with various f-vectors. We show…

The paper constructs new rational homology 3-spheres bounding rational homology 4-balls.

We determine the Christoffel's symbols for the Siegel-Jacobi ball endowed with the balanced metric. We study the equations of geodesics on the Siegel-Jacobi ball. We calculate the covariant derivative of one-forms in the variables in which is expressed the balanced metric on the Siegel-Jacobi ball.

The Farey tree helps embed rational balls and lens spaces into complex projective space.

4-ball can be tiled with knotted surfaces.

Unique ancient convex flow in a ball with free boundary found.

Study free boundary minimal submanifolds in geodesic balls in hyperbolic and spherical spaces.

In a compact orbifold, for small prescribed volume, an isoperimetric region is close to a small metric ball; in a Euclidean orbifold, it is a small metric ball.

Proves rigidity of maps between balls with Hölder boundary continuity.

No free boundary Möbius bands exist in a 3D ball.

Geodesic balls with non-negative Ricci curvature have a sharp lower bound on their first Dirichlet eigenvalue.

This paper classifies ball quotients of the complex projective plane.

A well-known and interesting family of sub-Riemannian space are the systems involving two balls rolling against each other without slipping or twisting. In this note, we show how the sub-Riemannian geodesics of these space, when the two balls are embedded in $\mathbb{R}^3 \times \mathbb{R}^3$, are horizontal curves on …

Round balls minimize liquid drop model volumes ≤ 1.

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

The small-ball method was introduced as a way of obtaining a high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions on the indexing class. The key assumption was that class members satisfy a uniform small-ball estimate: that $Pr(|f| \geq κ\|f\|_{L_2}) \geq δ$ for given const…

Investigate pseudoconvexity of locally trivial holomorphic ball bundles over compact Riemann surfaces.

Large PL surfaces in homology balls can have arbitrarily high genus.

We prove global estimates for the sub-Riemannian distance of CR Sasakian manifolds with non negative horizontal Webster-Tanaka Ricci curvature. In particular, in this setting, large sub-Riemannian balls are comparable to Riemannian balls.

Existence and instability of biharmonic maps from balls to spheres.

We study the number of distinct ways in which a smooth projective surface $X$ can be realized as a smooth toroidal compactification of a ball quotient. It follows from work of Hirzebruch that there are infinitely many distinct ball quotients with birational smooth toroidal compactifications. We take this to its natural…

Ball k-means reduces point-centroid distance computations for faster k-means clustering.