arXiv research

Paper proves uniqueness of minimal hypersurfaces in specific domains.

We construct open domains in Euclidean 3-space which do not admit complete properly immersed minimal surfaces with an annular end. These domains can not be smooth by a recent result of Martin and Morales

The study restricts surfaces in a specific geometry to certain configurations, proving no annular ends can be contained in horizontal slabs.

Paper constructs a spectral sequence linking annular Khovanov homology to reduced Khovanov homology.

New symplectic annular Khovanov homology connects knot theory to Floer homology.

Paper introduces new homology for links in an annulus.

Study shows links with unbounded annular Khovanov gradings but bounded Floer gradings.

Study on harmonic maps from surfaces with energy bounds and neck domains.

A triangulation of a compact 3-manifold is annular-efficient if it is 0-efficient and the only normal, incompressible annuli are thin edge-linking. If a compact 3-manifold has an annular-efficient triangulation, then it is irreducible, boundary-irreducible, and an-annular. Conversely, it is shown that for a compact, ir…

Study detects a specific type of link using annular Khovanov homology.

Refines quantum annular homology using stable homotopy methods.

We prove that given any compact Riemannian 3-manifold with boundary M, there exists a smooth properly embedded one-manifold G, included in M, each of whose components is a simple closed curve and such that the domain D=Int(M)-G does not admit any properly immersed open surfaces with at least one annular end, bounded me…

We introduce an sl(n) homology theory for knots and links in the thickened annulus. To do so, we first give a fresh perspective on sutured annular Khovanov homology, showing that its definition follows naturally from trace decategorifications of enhanced sl(2) foams and categorified quantum gl(m), via classical skew Ho…

We prove that the Khovanov-Lee complex of an oriented link, L, in a thickened annulus, A x I, has the structure of a bifiltered complex whose filtered chain homotopy type is an invariant of the isotopy class of L in A x I. Using ideas of Ozsvath-Stipsicz-Szabo as reinterpreted by Livingston, we use this structure to de…

New method associates annular links to elements of Thompson's group T.

Defines Khovanov homology with gl(1|1) action, preserving Reidemeister moves.

New annular link invariants from spectral sequence filtration.

New equivariant version of Khovanov homology for annuli.

The paper extends knot theory to annular and toroidal pseudo knots.

Extends quantum annular homology to infinite sets.

Study proves existence and nonexistence for annular surfaces with specific curvature and boundary.

Proves a conjecture for annular links using homology classes.

Lifts an $\mathfrak{sl}_2$ action to annular Khovanov homology's stable refinement.

Study annular concordance invariants and refine transverse link invariants.

Define web algebras for annular SL(2) and SL(3) using foam TQFTs.

Rigidity theorem for spherical sectors in Riemannian manifolds.

Study on shape optimization for specific eigenvalue problems on domains.

New stable homotopy refinement of quantum annular Khovanov homology.

The paper extends knot polynomials to annular and toroidal pseudo links.

In this article, we study the ramification of the Gauss map of complete minimal surfaces in R^m on annular ends. This work is a continuation of previous work of Dethloff-Ha. We thus give an improvement of the results on annular ends of complete minimal surfaces of Jin-Ru.

New link detection results using closures of 3-braids.

The paper finds the largest eigenvalue for a specific type of domain in hyperbolic space.

Let $\widetilde{K}$ be a two-periodic braid and let $K$ be its quotient. In this paper we show there is a spectral sequence from the next-to-top winding number grading of the sutured annular Khovanov homology of the closure of $\widetilde{K}$ to the next-to-top winding number grading of the sutured annular Khovanov hom…

Unified construction of link homologies using categorical annular evaluation.

The paper extends knotoid theory to annular and toroidal settings.

New structure for quantum algebra representations.

In this article, we study the ramification of the Gauss map of complete minimal surfaces in R^3 and R^4 on annular ends. We obtain results which are similar to the ones obtained by Fujimoto and Ru for (the whole) complete minimal surfaces, thus we show that the restriction of the Gauss map to an annular end of such a c…

Develops a new spectrum for annular links, recovering a transverse invariant at extreme gradings.

In this paper we describe the notion of an annular end of a Riemann surface being of finite type with respect to some harmonic function and prove some theoretical results relating the conformal structure of such an annular end to the level sets of the harmonic function. We then apply these results to understand and cha…

New invariants classify shapes of 3-braid closures.

We define a third grading on Khovanov homology, which is an invariant of annular links but changes by $\pm 1$ under stabilization. We illustrate the use of our computer implementation, and give some example calculations.

In this article, we study the modified defect relations of the Gauss map of complete minimal surfaces in $\mathbb R^3$ and $\mathbb R^4$ on annular ends. We obtain results which are similar to the ones obtained by Fujimoto~[J. Differential Geometry \textbf{29} (1989), 245-262] for (the whole) complete minimal surfaces…

We construct a braid conjugacy class invariant $κ$ by refining Plamenevskaya's transverse element $ψ$ in Khovanov homology via the annular grading. While $κ$ is not an invariant of transverse links, it distinguishes some braids whose closures share the same classical invariants but are not transversely isotopic. Using …

Short note observes quantum Hochschild homology as a composition of known operations.

This paper upgrades Khovanov homology to an L-infinity module structure.

Let L be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of the exterior current algebra of the Lie algebra sl_2. When L is an m-framed n-cable of a knot K in the three-sphere, its sutured annular Khovanov homology carries a commuting action of the symmetric group S_n…

This paper establishes that sutured annular Khovanov homology is not invariant for braid closures under axis-preserving mutations. This follows from an explicit relationship between sutured annular Khovanov homology and the classical Burau representation for braid closures.

In this paper we prove non-existence and classification results for elliptic fully nonlinear elliptic degenerate conformal equations on certain subdomains of the sphere with prescribed constant mean curvature along its boundary. We also consider non-degenerate equations. Such subdomains are the hemisphere (or a geodesi…