arXiv research

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

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

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

Study investigates minimal surfaces in spherical caps, extending previous findings.

New minimal surfaces found with spherical curvature lines.

The study finds the optimal metrics for free boundary minimal surfaces in spherical caps.

Classifies essential annuli in a genus two handlebody exterior.

Study minimal annuli in a slab, estimating their area.

Study proves uniqueness of certain minimal surfaces in spherical and hyperbolic spaces.

In this paper, we are interested in the construction of quasiconformal mappings between domains of the Heisenberg group H that minimise a mean distortion functional. We propose to construct such mappings by considering a corresponding problem between domains of Poincaré half-plane $\mathbb H$. The first map we construc…

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 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.

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…

Alexander polynomial derived from knot contact homology and Floer strips.

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

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…

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…

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

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 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.

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 study finds many Möbius bands and annuli on toroids.

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

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

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…

We analyze how a family of essential annuli in a compact 3-manifold will induce, from a strongly irreducible generalized Heegaard splitting of the ambient manifold, generalized Heegaard splittings of the complementary components. There are specific applications to the subadditivity of tunnel number of knots, improving …

Paper shows how to embed Möbius bands with many twists and small aspect ratios.

The paper examines how the first Steklov-Dirichlet eigenvalue changes with the distance between two concentric circles.

Every homeomorphism of Euclidean space is a commutator of two homeomorphisms.

The study finds no extremal metrics for eigenvalues on compact manifolds but constructs examples for annuli.

We show for $k \geq 2$ that the locally Lipschitz viscosity solution to the $σ_k$-Loewner-Nirenberg problem on a given annulus $\{a < |x| < b\}$ is $C^{1,\frac{1}{k}}_{\rm loc}$ in each of $\{a < |x| \leq \sqrt{ab}\}$ and $\{\sqrt{ab} \leq |x| < b\}$ and has a jump in radial derivative across $|x| = \sqrt{ab}$. Further…

Minimal surfaces span periodic curves in 3D space.

We study constant mean curvature 1/2 surfaces in H2xR that admit a compactification of the mean curvature operator. We show that a particular family of complete entire graphs over H2 admits a structure of infinite dimensional manifold with local control on the behaviors at infinity. These graphs also appear to have a h…