Related papers: Collared and non-collared manifold boundaries

This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.

We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.

We construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity.

We study the large-scale geometry of 3-manifolds with nontrivial 2-dimensional bounded cohomology, with a view to proving a weak version of the geometrization conjecture for such manifolds.

We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the…

The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open…

This paper, which is an outgrowth of a previous paper of the authors, continues the study of dimension 1 foliations on non-metrisable manifolds emphasising some anomalous behaviours. We exhibit surfaces with various extra properties like…

We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries

We give a generalization of Thurston's Bounded Image Theorem for skinning maps, which applies to pared 3-manifolds with incompressible boundary that are not necessarily acylindrical. Along the way we study properties of divergent sequences…

This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds endowed with two transversal Lagrangian foliations. We also study the non-integrable case (i.e., a symplectic manifold endowed with two transversal Lagrangian…

On any surface we give an example of a metric that contains simple closed geodesics with arbitrary high Morse index. Similarly, on any 3-manifold we give an example of a metric that contains embedded minimal tori with arbitrary high Morse…

We give examples of harmonic maps between negatively curved manifolds with special properties. These negatively curved manifolds do not have the homotopy type of a locally symmetric space.

In this paper we try to compare the "horoboundary" of a (not necessarily simply connected) negatively curved complete Riemannian manifold X with the visual one and describe with explicit examples some phenomenoms wich may appear when X is…

We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with…

We prove that a quasi-isometric map, and more generally a coarse embedding, between pinched Hadamard manifolds is within bounded distance from a unique harmonic map.

The aim of this paper is to provide a proof for a version of Morse inequality for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof…

In this paper, we study collapsed manifolds with boundary, where we assume a lower sectional curvature bound, two sides bounds on the second fundamental forms of boundaries and upper diameter bound. Our main concern is the case when inradii…

We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…

Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift

This paper generalizes the bordered-algebraic knot invariant introduced in an earlier paper, giving an invariant now with more algebraic structure. It also introduces signs to define these invariants with integral coefficients. We describe…