arXiv research

We show that after stabilizations of opposite parity and braid isotopy, any two braids in the same topological link type cobound embedded annuli. We use this to prove the generalized Jones conjecture relating the braid index and algebraic length of closed braids within a link type, following a reformulation of the prob…

Study on surfaces minimizing elastic energy with boundary constraints.

In previous work with Schoenfeld, we considered a string-type chain complex of curves on surfaces, with differential given by resolving crossings, and computed the homology of this complex for discs. In this paper we consider the corresponding "string homology" of annuli. We find this homology has a rich algebraic stru…

The paper studies cylindrical handlebody-knots of genus two with unique unknotting annuli and finds trivial symmetry groups.

Alexander polynomial derived from knot contact homology and Floer strips.

Classifies essential annuli in a genus two handlebody exterior.

We consider two natural classes of minimal laminations in three-manifolds. Both classes may be thought of as limits - in different senses - of embedded minimal disks. In both cases, we prove that, under a natural geometric assumption on the three-manifold, the leaves of these laminations are topologically either disks,…

Study minimal annuli in a slab, estimating their area.

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

Sharp lower bound found for area of vector fields on spherical annuli.

In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a finite power of the free homotopy class of a closed orbit of the flow. We show …

Minimal annuli constructed in PSL2 via variational method.

In $\mathbb{S}^2 \times \mathbb{R}$ there is a two-parameter family of properly embedded minimal annuli foliated by circles. In this paper we show that this family contains all properly embedded minimal annuli. We use the description of minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$ by periodic harmonic maps $G : \…

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

New minimal discs and annuli found in ellipsoids.

We prove that maximal annuli in $\mathbb{L}^{3}$ bounded by circles, straight lines or cone points in a pair of parallel spacelike planes are part of either a Lorentzian catenoid or a Lorentzian Riemann's example. We show that under the same boundary condition, the same conclusion holds even when the maximal annuli hav…

Classifies essential annuli in genus two handlebody-knots, determining hyperbolicity and constructing obstructions.

Improved flatness in annuli using PDE methods.

Study eigenvalues and eigenfunctions of fourth-order operators in annuli, proving optimal estimates and non-radiality.

Constructs minimal annuli with free boundary in hyperbolic 3-space.

Existence of minimal annuli in 3-sphere with boundary on geodesic spheres.

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…

We prove the existence of free boundary minimal annuli inside suitably convex subsets of three-dimensional Riemannian manifolds with nonnegative Ricci curvature $-$ including strictly convex domains of the Euclidean space $\mathbb{R}^3$.

The paper proves a statement about surfaces diffeomorphic to annuli.

A semigroup of annuli integrates a central extension of vector fields on S^1.

Constructs minimal surfaces near the boundary of a ball.

The paper classifies CMC free boundary hypersurfaces in rotational domains.

Optimal constants for isoperimetric inequalities involving Steklov eigenvalues on surfaces are determined.

We explicitly classify all $S^1$-invariant free boundary minimal annuli and Möbius bands in $\mathbb{B}^n$. This classification is obtained from an analysis of the spectrum of the Dirichlet-to-Neumann map for $S^1$-invariant metrics on the annulus and Möbius band. First, we determine the supremum of the $k$-th normaliz…

Proves a plumbing-multiplicative property of a Links-Gould invariant.

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

Let $h:X \to Y$ be a homeomorphism between hyperbolic surfaces with finite topology. If $h$ is homotopic to a holomorphic map, then every closed geodesic in $X$ is at least as long as the corresponding geodesic in $Y$, by the Schwarz Lemma. The converse holds trivially when $X$ and $Y$ are disks or annuli, and it holds…

We study minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$ of finite type by relating them to harmonic maps $\mathbb{C} \to \mathbb{S}^2$ of finite type. We rephrase an iteration by Pinkall-Sterling in terms of polynomial Killing fields. We discuss spectral curves, spectral data and the geometry of the isospectral set…

Study on exotic smooth embeddings of surfaces in 4-manifolds, revealing different properties and complexities.

Study links with annuli using sutured Floer homology.

In this paper we study the moduli space of properly Alexandrov-embedded, minimal annuli in $\mathbb{H}^2 \times \mathbb{R}$ with horizontal ends. We say that the ends are horizontal when they are graphs of $\mathcal{C}^{2, α}$ functions over $\partial_\infty \mathbb{H}^2$. Contrary to expectation, we show that one can …

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

The critical catenoid is uniquely determined by certain symmetries of its boundary.

New analysis of crushing surfaces of positive genus impacts triangulation complexity.

Solutions to a specific problem are shown to be locally Lipschitz but not differentiable.

We show a non existence result for solutions of the prescribed mean curvature equation in the product manifold $\mathbb{H}^2 \times \R$, where $\mathbb{H}^2$ is the real hyperbolic plane. More precisely we prove a-priori estimates for graphs with constant mean curvature $h \in (0, 1/2]$ on circular annuli of $\mathbb{H…

The paper explores geometric properties of free boundary hypersurfaces in balls.

The study finds many Möbius bands and annuli on toroids.

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

Strict convexity is essential for compact minimal surfaces in curved spaces.

Researchers prove rigidity of first conformal Steklov eigenvalue on specific shapes.

We present a proof of the generalized Nitsche's conjecture proposed by W.H.Meeks III and H. Rosenberg: For $t\ge 0$, let $P_t$ denote the horizontal plane of height $t$ over the $x_1,x_2$ plane. Suppose that $M \subset R^3$ is a minimal annulus with the boundary contains in $P_0$ and that $M$ intersects every $P_t$ in …

We construct two one-parameter families of minimal properly embedded surfaces in the Lie group Sol3 using a Weierstrass-type representation. These surfaces are not invariant by a one-parameter group of ambient isometries. The first one can be viewed as a family of helicoids, and the second one is a family of minimal an…