arXiv research

Classifies conformal actions on essential 3D Riemannian spaces.

L-space knots lack essential Conway spheres, proven with Floer theory.

The paper studies essential spectra of submanifolds in Euclidean spaces.

Computes expected number of real intersection points of essential variety with random linear spaces.

Study submanifolds in hyperbolic space, focusing on their boundary and Laplace operator.

Two-dimensional collapsed spaces with lower Ricci bounds are topological surfaces.

In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essential coverings by contractible metric balls, and provide a uniform bound on the numbers of contractible metric balls formi…

In this article we prove a generalization of Weyl's criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over open manifolds and get new results for its essential spectrum.

Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.

Study on conformal transformations of Cahen-Wallach spaces, focusing on fixed points and discontinuous groups.

Classifies 1-connected Lorentzian manifolds with essential conformal groups.

Essential tori in certain 3-manifolds are missed by ideal points in character varieties.

Universal Bayes consistency proved in metric spaces.

We describe spaces of essential finite height (measured) laminations in a surface $S$ using a parameter space we call $\mathbb S$, an ordered semi-ring. We show that for every finite height essential lamination $L$ in $S$, there is an action of $π_1(S)$ on an $\mathbb S$-tree dual to the lift of $L$ to the universal co…

We construct an algorithm that lists all closed essential surfaces in the complement of a knot that lies on the fiber of a trefoil or figure eight knot. Such knots are Berge knots and hence admit lens space surgeries. Furthermore they may have arbitrarily large hyperbolic volume. Using this algorithm we concoct large v…

Tollefson described a variant of normal surface theory for 3-manifolds, called Q-theory, where only the quadrilateral coordinates are used. Suppose $M$ is a triangulated, compact, irreducible, boundary-irreducible 3-manifold. In Q-theory, if $M$ contains an essential surface, then the projective solution space has an e…

In this paper we investigate the relationship between a general existence of transport maps of optimal couplings with absolutely continuous first marginal and the property of the background measure called essentially non-branching introduced by Rajala-Sturm (Calc.Var.PDE 2014). In particular, it is shown that the quali…

In this paper we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplacian contains an interval. The results presented in this paper allow to determine the spectrum of the Lapla…

We establish a Lehto--Virtanen-type theorem and a rescaling principle for an isolated essential singularity of a holomorphic curve in a complex space, which are useful for establishing a big Picard-type theorem and a big Brody-type one for holomorphic curves.

Using Hirasawa-Murasugi's classification of fibered Montesinos knots we classify the L-space Montesinos knots, providing further evidence towards a conjecture of Lidman-Moore that L-space knots have no essential Conway spheres. In the process, we classify the fibered Montesinos knots whose open books support the tight …

Sharp eigenvalue bounds on metric measure spaces extend Cheng's theorem.

Constructs geometries with nonvanishing curvature and essential automorphisms.

We study torsion properties of the twisted Alexander modules of the affine complement $M$ of a complex essential hyperplane arrangement, as well as those of punctured stratified tubular neighborhoods of complex essential hyperplane arrangements. We investigate divisibility properties between the twisted Alexander polyn…

We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."

Essential dimension of a family of complex manifolds is the dimension of the image of its base in the Kuranishi space of the fiber. We prove that any family of hyperkähler manifolds over a compact simply connected base has essential dimension not greater than $1$. A similar result about families of complex tori is also…

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential self-adjointness of such operators to a negligible boundary property. When the operator…

We prove the existence of essential loops in the space of contact structures on torus bundles over the circle.

In this paper, we use normal surface theory to study Dehn filling on a knot-manifold. First, it is shown that there is a finite computable set of slopes on the boundary of a knot-manifold that bound normal and almost normal surfaces in a one-vertex triangulation of that knot-manifold. This is combined with existence th…

Essential self-adjointness and spectrum of CR GJMS operator proved.

Study essentiality and simplicial volume of manifolds fibered over spheres.

We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show its dense range in L^2 wh…

We extend the classical theory of isothermic surfaces in conformal 3-space, due to Bour, Christoffel, Darboux, Bianchi and others, to the more general context of submanifolds of symmetric $R$-spaces with essentially no loss of integrable structure.

Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.

Study cohomogeneity one RCD-spaces, proving structural results and constructing new examples.

We give an algorithm to find vertical essential tori in small Seifert fiber spaces with infinite fundamental groups. This implies that there are algorithms to decide whether a 3-manifold is a Seifert fiber space.

Proves weakly non-collapsed RCD spaces are strongly non-collapsed.

Introduces new limit spaces for degenerating Calabi-Yau families.

4-manifolds with non-positive curvature are essentially Euclidean.

We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.

In this paper we study the relation between two diagrammatic representations of links in lens spaces: the disk diagram and the grid diagram and we find how to pass from one to the other. We also investigate whether the HOMFLY-PT invariant and the Link Floer Homology are essential invariants, that is, we try to understa…

Using the theory of Weyl structures, we give a natural generalization of the notion of essential conformal structures and conformal Killing fields to arbitrary parabolic geometries. We show that a parabolic structure is inessential whenever the automorphism group acts properly on the base space. As a corollary of the g…

The paper studies properties of $\mathrm{RCD}(K,N)$ spaces and their boundaries.

Developed theory for Thurston maps with a small set of essential singularities.

In this paper we study the Ricci flow on compact four-manifolds with positive isotropic curvature and with no essential incompressible space form. Our purpose is two-fold. One is to give a complete proof of Hamilton's classification theorem on four-manifolds with positive isotropic curvature and with no essential incom…

We consider the Dirichlet Laplacian in tubular neighbourhoods of complete non-compact Riemannian manifolds immersed in the Euclidean space. We show that the essential spectrum coincides with the spectrum of a planar tube provided that the second fundamental form of the manifold vanishes at infinity and the transport of…

We prove a rigidity of the lightcone in Minkowski space. It is essentially the unique space endowed with a degenerate Riemannian metric, of lightlike type, and supporting an isometric non-proper action of a semi-simple group.

We show that mapping class groups associated to all types of real algebraic curves are virtual duality groups. We also deduce some results about the orbifold homotopy groups of the moduli spaces of real algebraic curves. We achieve these results by defining a new complex associated to a not necessarily orientable surfa…

Proves metric measure spaces with certain properties are one-dimensional.